testbookLayout.git

parent: fcf12275 | 补丁 | 提交 | ignore whitespace

Merge branch 'master' of http://182.92.203.7:2001/r/testbookLayout

zhongshujie

2024-10-22 51ad6706fed4b080b0cb1bb771028a551b9ec27c

Merge branch 'master' of http://182.92.203.7:2001/r/testbookLayout

12个文件已修改

1个文件已添加

	.env.product	10 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/App.vue	3 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/civilAviation/view/components/index.vue	6 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/assets/main.less	26 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/chapter001.vue	28 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/chapter002.vue	2115 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/chapter003.vue	2527 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/chapter004.vue	4707 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/chapter005.vue	6774 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/header.vue	2 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/books/mathBook/view/components/index.vue	188 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/components/calculator/index.vue	58 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史
	src/components/examinations/index.vue	60 ●●●●● 补丁 \| 查看 \| 原始文档 \| blame \| 历史

 .env.product

@@ -1,8 +1,8 @@
VUE_APP_ENV = 'product'
VUE_APP_API_URL = "https://jsek.bnuic.com"
# VUE_APP_RESOURCE_CTX = 'https://jsek.bnuic.com/books/resource/'
# VUE_APP_PUBLIC_PATH = 'https://jsek.bnuic.com/books/book/botany'
VUE_APP_RESOURCE_CTX = 'http://182.92.203.7:3007/books/resource/'
VUE_APP_PUBLIC_PATH = 'http://182.92.203.7:3007/books/book/botany'
VUE_APP_RESOURCE_CTX = 'https://jsek.bnuic.com/books/resource/'
VUE_APP_PUBLIC_PATH = 'https://jsek.bnuic.com/books/book/mathBook'
# VUE_APP_RESOURCE_CTX = 'http://182.92.203.7:3007/books/resource/'
# VUE_APP_PUBLIC_PATH = 'http://182.92.203.7:3007/books/book/botany'
VUE_APP_BOOK_LIST = "childHealth/lifeCare/sportsAndHealth/embedded/english/artAndDance/artAndDrama/mathBook/botany"
VUE_APP_BOOK_ID = 'botany'
VUE_APP_BOOK_ID = 'mathBook'

 src/App.vue

@@ -64,12 +64,11 @@
      // artAndDrama
      // mathBook
      // civilAviation

      this.activeBook = await this.config.getBookConfig(
      process.env.VUE_APP_RESOURCE_CTX +
        (process.env.VUE_APP_ENV == "product"
          ? process.env.VUE_APP_BOOK_ID
          : "civilAviation")
          : "mathBook")
      );

      // this.activeBook = await this.config.getBookConfig(

 src/books/civilAviation/view/components/index.vue

@@ -94,6 +94,7 @@
    // 默认加载章节
    this.showCatalogList = [1];
    // 滚动监听节流
    debugger
    this.throttledScrollHandler = _.throttle(
      this.scrollFun,
      this.throttleThreshold,
@@ -198,6 +199,8 @@
    scrollFun(event) {
      this.handleVideoPicture()
      // 判断向上滚动还是向下滚动
      console.log(11);
      
      if (event.target.scrollTop > this.previousScrollTop) {
        this.getAduio();
        // 向下
@@ -207,6 +210,9 @@
          currentScrollTop >=
          event.target.scrollHeight - this.loadThreshold
        ) {
          console.log(1);
          
          debugger
          // 到达阈值
          if (
            this.showCatalogList[this.showCatalogList.length - 1] <

 src/books/mathBook/assets/main.less

@@ -430,7 +430,7 @@
  .page-box {
    position: relative;
    box-sizing: border-box;
    min-height: 1150px;
    min-height: 1120px;
    margin-bottom: 20px;
    box-shadow: 0 3px 6px 1px #00000029;
    background-color: #fff;
@@ -557,6 +557,9 @@
  .t0 {
    text-indent: 0;
  }
  .t1 {
    text-indent: 1em;
  }
  .t- {
    text-indent: 0.5em;
  }
@@ -580,7 +583,7 @@
  }
  .page-box {
    box-sizing: border-box;
    min-height: 1150px;
    min-height: 1120px;
    margin-bottom: 20px;
    box-shadow: 0 3px 6px 1px #00000029;
    background-color: #fff;
@@ -701,6 +704,9 @@
  }
  .mt-40 {
    margin-top: 40px;
  }
  .mt-60 {
    margin-top: 60px !important;
  }
  .mt-80 {
    margin-top: 80px !important;
@@ -854,6 +860,22 @@
    height: 0 !important;
    box-shadow: none !important;
  }
  // 带按钮p标签
  .p-btn {
    display: flex;
    justify-content: left;
    align-items: center;
    flex-wrap: wrap;
    i {
      text-indent: 0;
    }
  }
  .iframe-box {
    width: 100%;
    min-height: 800px;
    border: 1px solid #00a1e9;
    border-radius: 10px;
  }
}

/* 媒体查询做基础响应式布局 */

 src/books/mathBook/view/components/chapter001.vue

@@ -1,5 +1,5 @@
<template>
  <div class="chapter" num="1">
  <div class="chapter" num="2">
    <div class="page-box" page="8">
      <div v-if="showPageList.indexOf(8) > -1">
        <h1 id="a007">
@@ -67,7 +67,7 @@
          </p>
          <p>（2） 0～10中的所有奇数；</p>
          <p>（3） 我国农历二十四节气；</p>
          <p>（4） 方程x2-5x-6=0的解；</p>
          <p>（4） 方程<i>x</i><sup>2</sup>-5<i>x</i>-6=0的解；</p>
          <p>（5） 到一个角的两边距离相等的所有点.</p>

          <p class="left">
@@ -804,16 +804,14 @@
        </ul>
        <div class="padding-116">
          <div class="center openImgBox">
            <img class="img-c" alt="" src="../../assets/images/0023-1.jpg" style="margin-top: 30px" />
            <img class="img-b" alt="" src="../../assets/images/0023-1.jpg" style="margin-top: 30px" />
            <p class="img" style="font-size: 14px">图1-4</p>
          </div>

          <p>根据子集的定义，任何一个集合A都是它自身的子集，即A⊆A.</p>
          <p>
            我们规定：<b>空集是任何集合的子集</b>
            ，即对于任何一个集合A，都有∅⊆A.
          </p>

          <div class="img-float openImgBox">
            <img class="img-c" alt="" src="../../assets/images/0023-2.jpg" />
            <p class="img" style="font-size: 14px">图1-5</p>
@@ -858,7 +856,6 @@
              </p>
            </li>
          </ul>

          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
@@ -2101,24 +2098,6 @@
    <!-- 030 -->
    <div class="page-box hidePage" page="37">
    </div>

    <!-- 函数控件弹窗 -->
    <el-dialog :visible.sync="dialogVisible" width="60%" :append-to-body="true" :show-close="false">
      <div slot="title" style="padding: 0 0 15px 0; position: relative">
        <svg style="position: absolute; right: 10px; cursor: pointer" @click="dialogVisible = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797" p-id="4253"></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797" p-id="4254"></path>
        </svg>
      </div>
      <iframe src="https://www.geogebra.org/calculator" frameborder="0" style="width: 100%; min-height: 800px"></iframe>
    </el-dialog>

    <!-- 解题思路弹窗 -->
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false" @close="closeDialog" class="thinkDialog" >
      <div slot="title" class="think-header" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
@@ -2248,7 +2227,6 @@
      },
      collectImg: require('../../assets/images/icon/heart.png'),
      collectCheck: require('../../assets/images/icon/heart-check.png'),
      dialogVisible: false,
      thinkingDialog: false,
      videoPath: '',
      stepIndex: 1,

 src/books/mathBook/view/components/chapter002.vue

@@ -1,5 +1,5 @@
<template>
  <div class="chapter" num="2">
  <div class="chapter" num="3">
    <!-- 第二单元首页 -->
    <div class="page-box" page="38">
      <div v-if="showPageList.indexOf(38) > -1">
@@ -274,27 +274,70 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　已知<i>a</i>＞<i>b</i>＞0.
          </p>
          <p>（1） 比较2<i>a</i>与2<i>b</i>的大小；</p>
          <p>（2） 比较-2<i>a</i>与-2<i>b</i>的大小；</p>
          <p>（3） 比较<i>ac</i>与<i>bc</i>的大小.</p>
          <p>
          <p class="p-btn">
            （1） 比较2a与2b的大小；
            <span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer0">
            <span class="zt-ls"><b>解</b></span>（1） 因为<i>a</i>＞<i>b</i>，2＞0，根据性质2，有2<i>a</i>＞2<i>b</i>.
          </p>
          <p>
          <p class="p-btn">
            （2） 比较-2a与-2b的大小；
            <span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer1">
            <span class="zt-ls"><b>解</b></span>
            （2）
            因为<i>a</i>＞<i>b</i>，-2＜0，根据性质3，有-2<i>a</i>＜-2<i>b</i>.
          </p>
          <p>（3） 若<i>c</i>＞0，根据性质2，有<i>ac</i>＞<i>bc</i>.</p>
          <p>若<i>c</i>＜0，根据性质3，有<i>ac</i>＜<i>bc</i>.</p>
          <p>若<i>c</i>=0，则有<i>ac</i>=<i>bc</i>=0，所以<i>ac</i>=<i>bc</i>.</p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　已知<i>a</i>＞<i>b</i>，比较<i>a</i>-1与<i>b</i>-2的大小.
          <p class="p-btn">
            （3） 比较ac与bc的大小.
            <span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span> 因为<i>a</i>＞<i>b</i>，-1＞-2，
          <div v-if="isShowAnswer2">
            <p>
              <span class="zt-ls"><b>解</b></span>
              （3） 若<i>c</i>＞0，根据性质2，有<i>ac</i>＞<i>bc</i>.
            </p>
            <p>若<i>c</i>＜0，根据性质3，有<i>ac</i>＜<i>bc</i>.</p>
            <p>若<i>c</i>=0，则有<i>ac</i>=<i>bc</i>=0，所以<i>ac</i>=<i>bc</i>.</p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例2</b></span>
            <span class="t1">已知a＞b，比较a-1与b-2的大小.</span>
            <span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>根据推论1，有<i>a</i>+（-1）＞<i>b</i>+（-2），</p>
          <p>即<i>a</i>-1＞<i>b</i>-2.</p>
          <div v-if="isShowAnswer3">
            <p>
              <span class="zt-ls"><b>解</b></span> 因为<i>a</i>＞<i>b</i>，-1＞-2，
            </p>
            <p>根据推论1，有<i>a</i>+（-1）＞<i>b</i>+（-2），</p>
            <p>即<i>a</i>-1＞<i>b</i>-2.</p>
          </div>
        </div>
      </div>
    </div>
@@ -332,100 +375,110 @@
          <p>
            因为（<i>a</i><sup>2</sup>+1）-2<i>a</i>=<i>a</i><sup>2</sup>-2<i>a</i>+1=（<i>a</i>-1）<sup>2</sup>，且当<i>a</i>≠1时，（<i>a</i>-1）<sup>2</sup>＞0，所以<i>a</i><sup>2</sup>+1＞2<i>a</i>.
          </p>
          <p>
            <span class="zt-ls"><b>例1</b></span>　分析本节“问题提出”中的问题.
          <p class="p-btn">
            <span class="zt-ls"><b>例1</b></span>　
            <span class="t1">分析本节“问题提出”中的问题.</span>
            <span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span> 作差可得<math display="0">
              <mfrac>
                <mn>98</mn>
                <mn>166</mn>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mrow>
          <div v-if="isShowAnswer4">
            <p>
              <span class="zt-ls"><b>解</b></span> 作差可得<math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mo>+</mo>
                  <mn>8</mn>
                </mrow>
                <mrow>
                  <mn>166</mn>
                  <mo>+</mo>
                  <mn>8</mn>
                </mrow>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mn>98</mn>
                <mn>166</mn>
              </mfrac>
              <mo>−</mo>
              <mfrac>
                <mn>106</mn>
                <mn>174</mn>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mn>98</mn>
                    <mo>+</mo>
                    <mn>8</mn>
                  </mrow>
                  <mrow>
                    <mn>166</mn>
                    <mo>+</mo>
                    <mn>8</mn>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mn>98</mn>
                  <mo>×</mo>
                  <mn>174</mn>
                  <mo>−</mo>
                  <mn>166</mn>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mn>106</mn>
                  <mo>×</mo>
                  <mn>166</mn>
                </mrow>
                <mrow>
                  <mn>166</mn>
                  <mo>×</mo>
                  <mn>174</mn>
                </mrow>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mrow>
                  <mo>−</mo>
                  <mn>544</mn>
                </mrow>
                <mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mn>98</mn>
                    <mo>×</mo>
                    <mn>174</mn>
                    <mo>−</mo>
                    <mn>106</mn>
                    <mo>×</mo>
                    <mn>166</mn>
                  </mrow>
                  <mrow>
                    <mn>166</mn>
                    <mo>×</mo>
                    <mn>174</mn>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mo>−</mo>
                    <mn>544</mn>
                  </mrow>
                  <mrow>
                    <mn>166</mn>
                    <mo>×</mo>
                    <mn>174</mn>
                  </mrow>
                </mfrac>
                <mo>＜</mo>
                <mn>0</mn>
              </math>，所以<math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                  <mo>×</mo>
                </mfrac>
                <mo>＜</mo>
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mrow>
              </mfrac>
              <mo>＜</mo>
              <mn>0</mn>
            </math>，所以<math display="0">
              <mfrac>
                <mn>98</mn>
                <mn>166</mn>
              </mfrac>
              <mo>＜</mo>
              <mfrac>
                <mn>106</mn>
                <mn>174</mn>
              </mfrac>
            </math>.
          </p>
          <p>
            又因为<math display="0">
              <mfrac>
                <mn>98</mn>
                <mn>166</mn>
              </mfrac>
              <mo>≈</mo>
              <mn>0.590</mn>
              <mn>4</mn>
            </math>，<math display="0">
              <mfrac>
                <mn>106</mn>
                <mn>174</mn>
              </mfrac>
              <mo>≈</mo>
              <mn>0.690</mn>
              <mn>2</mn>
            </math>，所以立起脚尖后，该芭蕾舞演员的下半身长与全身长的比值更接近0.618.
          </p>
                </mfrac>
              </math>.
            </p>
            <p>
              又因为<math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>≈</mo>
                <mn>0.590</mn>
                <mn>4</mn>
              </math>，<math display="0">
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>≈</mo>
                <mn>0.690</mn>
                <mn>2</mn>
              </math>，所以立起脚尖后，该芭蕾舞演员的下半身长与全身长的比值更接近0.618.
            </p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left">
@@ -521,9 +574,10 @@
              </math>.
            </p>
          </div>

          <p>
            <span class="zt-ls"><b>例2</b></span>　已知<i>b</i>＞<i>a</i>＞0，<i>c</i>＞0，比较<math display="0">
          <p class="p-btn">
            <span class="zt-ls"><b>例2</b></span>
            <span calss="t1">已知b＞a＞0，c＞0，比较</span>
            <math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
@@ -542,166 +596,175 @@
                <mi>b</mi>
              </mfrac>
            </math>的大小.
            <span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span> 作差可得<math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
                <mrow>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mi>a</mi>
                <mi>b</mi>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mrow>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
          <div v-if="isShowAnswer5">
            <p>
              <span class="zt-ls"><b>解</b></span> 作差可得<math display="0">
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                  <mi>b</mi>
                </mrow>
                <mrow>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                  <mi>b</mi>
                </mrow>
              </mfrac>
              <mo>−</mo>
              <mfrac>
                <mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mi>a</mi>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                </mrow>
                <mrow>
                  <mi>b</mi>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>a</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                </mrow>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mrow>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                    <mo>−</mo>
                  </mrow>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                  </mrow>
                  <mi>c</mi>
                </mrow>
                <mrow>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>−</mo>
                      <mi>a</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>c</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                  <mi>b</mi>
                </mrow>
              </mfrac>
            </math>.
          </p>
          <p>
            因为<i>b</i>＞<i>a</i>＞0，所以<i>b</i>-<i>a</i>＞0.又因为<i>c</i>＞0，所以<math display="0">
              <mfrac>
                <mrow>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                    <mo>−</mo>
                  </mrow>
                </mfrac>
              </math>.
            </p>
            <p>
              因为<i>b</i>＞<i>a</i>＞0，所以<i>b</i>-<i>a</i>＞0.又因为<i>c</i>＞0，所以<math display="0">
                <mfrac>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>−</mo>
                      <mi>a</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                  </mrow>
                </mfrac>
                <mo>＞</mo>
                <mn>0</mn>
              </math>，
            </p>
            <p>
              即<math display="0">
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                  <mi>c</mi>
                </mrow>
                <mrow>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                  <mi>b</mi>
                </mrow>
              </mfrac>
              <mo>＞</mo>
              <mn>0</mn>
            </math>，
          </p>
          <p>
            即<math display="0">
              <mfrac>
                <mrow>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
                <mrow>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
              </mfrac>
              <mo>−</mo>
              <mfrac>
                <mi>a</mi>
                <mi>b</mi>
              </mfrac>
              <mo>＞</mo>
              <mn>0</mn>
            </math>，所以<math display="0">
              <mfrac>
                <mrow>
                </mfrac>
                <mo>＞</mo>
                <mn>0</mn>
              </math>，所以<math display="0">
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                </mfrac>
                <mo>＞</mo>
                <mfrac>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
                <mrow>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
              </mfrac>
              <mo>＞</mo>
              <mfrac>
                <mi>a</mi>
                <mi>b</mi>
              </mfrac>
            </math>.
          </p>
                </mfrac>
              </math>.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
@@ -803,7 +866,7 @@
            <p>第二单元 不等式</p>
          </li>
          <li>
            <p><span>039</span></p>
            <p><span>039-041</span></p>
          </li>
        </ul>
        <div class="padding-116">
@@ -817,8 +880,16 @@
              区间也是一个集合，它是实数集的一个子集.但并非所有的数集都能用区间表示.例如，集合{1，3，4，5，7，8，11，12}、自然数集<b>N</b>、整数集<b>Z</b>就不能用区间表示.
            </p>
          </div>
          <p>
            <span class="zt-ls"><b>例1</b></span>　把下列集合用区间表示出来，并指出区间的类型.
          <p class="p-btn">
            <span class="zt-ls"><b>例1</b></span>
            <span class="t1">把下列集合用区间表示出来，并指出区间的类型.</span>
            <span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>（1） {<i>x</i>|-3≤<i>x</i>≤1}；（2） {<i>x</i>|-1＜<i>x</i>＜2}；</p>
          <p>
@@ -863,105 +934,114 @@
            </math>；
          </p>
          <p>（5） {<i>x</i>|<i>x</i>≥2}；（6） {<i>x</i>|<i>x</i>＜1}.</p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1） ［-3，1］，是闭区间；
          <div v-if="isShowAnswer6">
            <p>
              <span class="zt-ls"><b>解</b></span>（1） ［-3，1］，是闭区间；
            </p>
            <p>（2）（-1，2），是开区间；</p>
            <p>
              （3）
              <math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">[</mo>
                  <mfrac>
                    <mn>3</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo>，</mo>
                  <mn>4</mn>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，是左闭右开区间；
            </p>
            <p>
              （4）
              <math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mn>6</mn>
                  <mo>，</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">]</mo>
                </mrow>
              </math>，是左开右闭区间；
            </p>
            <p>（5） ［2，+∞），是左闭右开区间；</p>
            <p>（6）（-∞，1），是开区间.</p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例2</b></span>
            <span class="t1">用区间表示不等式3<i>x</i>＜9<i>x</i>+4的解集，并在数轴上表示出来.</span>
            <span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>（2）（-1，2），是开区间；</p>
          <p>
            （3）
            <math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">[</mo>
                <mfrac>
                  <mn>3</mn>
                  <mn>2</mn>
                </mfrac>
                <mo>，</mo>
                <mn>4</mn>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，是左闭右开区间；
          <div v-if="isShowAnswer7">
            <p>
              <span class="zt-ls"><b>解</b></span> 解不等式3<i>x</i>＜9<i>x</i>+4，得
            </p>
            <math display="block">
              <mi>x</mi>
              <mo>＞</mo>
              <mo>−</mo>
              <mfrac>
                <mn>2</mn>
                <mn>3</mn>
              </mfrac>
              <mo>.</mo>
            </math>
            <p>
              所以不等式的解集用区间表示为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>2</mn>
                    <mn>3</mn>
                  </mfrac>
                  <mo>，</mo>
                  <mo>+</mo>
                  <mi mathvariant="normal">∞</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，表示在数轴上如图2-1所示.
            </p>
            <p class="center"><img class="img-f" alt="" src="../../assets/images/0050-7.jpg" /></p>
            <p class="img">图2-1</p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例3</b></span>
            <span class="t1">设<b>R</b>为全集，集合A={x|-5＜x＜6}，B={x|x≥3或x≤-3}，用区间表示A∩B.</span>　
            <span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （4）
            <math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
                <mn>6</mn>
                <mo>，</mo>
                <mo>−</mo>
                <mfrac>
                  <mn>1</mn>
                  <mn>2</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">]</mo>
              </mrow>
            </math>，是左开右闭区间；
          </p>
          <p>（5） ［2，+∞），是左闭右开区间；</p>
          <p>（6）（-∞，1），是开区间.</p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　用区间表示不等式3<i>x</i>＜9<i>x</i>+4的解集，并在数轴上表示出来.
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span> 解不等式3<i>x</i>＜9<i>x</i>+4，得
          </p>
          <math display="block">
            <mi>x</mi>
            <mo>＞</mo>
            <mo>−</mo>
            <mfrac>
              <mn>2</mn>
              <mn>3</mn>
            </mfrac>
            <mo>.</mo>
          </math>
          <p>
            所以不等式的解集用区间表示为<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
                <mfrac>
                  <mn>2</mn>
                  <mn>3</mn>
                </mfrac>
                <mo>，</mo>
                <mo>+</mo>
                <mi mathvariant="normal">∞</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，表示在数轴上如图2-1所示.
          </p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0050-7.jpg" /></p>
          <p class="img">图2-1</p>
          <p>
            <span
              class="zt-ls"><b>例3</b></span>　设<b>R</b>为全集，集合<i>A</i>={<i>x</i>|-5＜<i>x</i>＜6}，<i>B</i>={<i>x</i>|<i>x</i>≥3或<i>x</i>≤-3}，用区间表示<i>A</i>∩<i>B</i>.
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>
            在数轴上将集合<i>A</i>，<i>B</i>表示出来，如图2-2所示.
          </p>
          <p class="center"><img class="img-d" alt="" src="../../assets/images/0050-8.jpg" /></p>
          <p class="img">图2-2</p>
          <p>
            <i>A</i>∩<i>B</i>={<i>x</i>|-5＜<i>x</i>＜6}∩{<i>x</i>|<i>x</i>≥3或<i>x</i>≤-3}
          </p>
          <p>={<i>x</i>|-5＜<i>x</i>≤-3}∪{<i>x</i>|3≤<i>x</i>＜6}</p>
          <p>=（-5，-3］∪［3，6）.</p>
        </div>
      </div>
    </div>
    <!-- 040 -->
    <div class="page-box" page="47">
      <div v-if="showPageList.indexOf(47) > -1">
        <ul class="page-header-odd fl al-end">
          <li>040-041</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <div v-if="isShowAnswer8">
            <p>
              <span class="zt-ls"><b>解</b></span>
              在数轴上将集合<i>A</i>，<i>B</i>表示出来，如图2-2所示.
            </p>
            <p class="center"><img class="img-d" alt="" src="../../assets/images/0050-8.jpg" /></p>
            <p class="img">图2-2</p>
            <p>
              <i>A</i>∩<i>B</i>={<i>x</i>|-5＜<i>x</i>＜6}∩{<i>x</i>|<i>x</i>≥3或<i>x</i>≤-3}
            </p>
            <p>={<i>x</i>|-5＜<i>x</i>≤-3}∪{<i>x</i>|3≤<i>x</i>＜6}</p>
            <p>=（-5，-3］∪［3，6）.</p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
@@ -971,8 +1051,8 @@
          </div>
          <h3 id="c015">习题2.2<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[47] ? questionData[47][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
            <examinations :cardList="questionData[47] ? questionData[47][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h2 id="b009">
            2.3 一元二次不等式<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
@@ -995,6 +1075,9 @@
          </p>
        </div>
      </div>
    </div>
    <!-- 040 -->
    <div class="page-box hidePage" page="47">
    </div>
    <!-- 041 -->
    <div class="page-box hidePage" page="48">
@@ -1135,24 +1218,135 @@
              </math>，与<i>y</i>轴的交点坐标为（0，<i>c</i>）.
            </p>
          </div>
          <p><b>例</b> 已知二次函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3，</p>
          <p>（1） 画出该函数图像；</p>
          <p>
          <p class="p-btn">
            <b>例</b>
            <span>已知二次函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3，</span>
            <span class="btn-box" @click="openDialog(thinkOne)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            （1） 画出该函数图像；
            <span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer9">
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0055-1.jpg" /></p>
            <p class="img">图2-3</p>
            <p>
              <span class="zt-ls"><b>解</b></span>（1） 因为<i>a</i>=1＞0，所以函数图像为开口向上的抛物线.
            </p>
            <p>
              因为<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-2）<sup>2</sup>-4×1×（-3）=16＞0，
            </p>
            <p>
              所以一元二次方程<i>x</i><sup>2</sup>-2<i>x</i>-3=0有两个不相等的实数解.
            </p>
            <p>解方程，得<i>x</i><sub>1</sub>=-1，<i>x</i><sub>2</sub>=3.</p>
            <p>所以抛物线与<i>x</i>轴的交点坐标为（-1，0），（3，0）.</p>
            <p>
              抛物线的顶点坐标为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mi>b</mi>
                    <mrow>
                      <mn>2</mn>
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo>，</mo>
                  <mfrac>
                    <mrow>
                      <mn>4</mn>
                      <mi>a</mi>
                      <mi>c</mi>
                      <mo>−</mo>
                      <msup>
                        <mi>b</mi>
                        <mrow>
                          <mn>2</mn>
                        </mrow>
                      </msup>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，即（1，-4）.
            </p>
            <p>
              抛物线的对称轴方程为<math display="0">
                <mi>x</mi>
                <mo>=</mo>
                <mo>−</mo>
                <mfrac>
                  <mi>b</mi>
                  <mrow>
                    <mn>2</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
              </math>，即<i>x</i>=1.抛物线与<i>y</i>轴的交点坐标为（0，<i>c</i>），即（0，-3）.根据函数的对称性，可以再取一些点，如（2，-3）.
            </p>
            <p>
              根据以上信息，就可以画出函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3的图像（如图2-3所示）.
            </p>
          </div>
          <p class="p-btn">
            （2）
            指出该函数图像上纵坐标分别为<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0的所有点；
            指出该函数图像上纵坐标分别为y=0，y＞0，y＜0的所有点；
            <span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer10">
            <span class="zt-ls"><b>解</b></span>
            （2）
            观察图像可知，满足<i>y</i>=0的点是抛物线与<i>x</i>轴的交点；满足<i>y</i>＞0的点是抛物线在<i>x</i>轴上方的所有点；满足<i>y</i>＜0的点是抛物线在<i>x</i>轴下方的所有点.
          </p>
          <p class="p-btn">
            （3）
            根据函数图像写出<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0时所对应的<i>x</i>的值或取值范围.
            根据函数图像写出y=0，y＞0，y＜0时所对应的x的值或取值范围.
            <span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span
              class="zt-ls2"><b>分析</b></span>　①根据<i>x</i><sup>2</sup>的系数判断函数图像（抛物线）的开口方向；②用判别式判定出一元二次方程<i>x</i><sup>2</sup>-2<i>x</i>-3=0的解的情况，从而确定二次函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3的图像与<i>x</i>轴的交点个数和交点坐标；③计算二次函数图像的顶点坐标、与<i>y</i>轴的交点坐标；④求出二次函数图像的对称轴方程，并利用函数图像的对称性再找出一些点；⑤最后根据上述信息画出函数图像.
          </p>
          <p class="block">
            画出图像后，<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0分别对应函数图像与<i>x</i>轴相交、函数图像在<i>x</i>轴上方、函数图像在<i>x</i>轴下方三种情形，根据图像完成（2）（3）
            两个问题.
          </p>
          <div v-if="isShowAnswer11">
            <p>
              <span class="zt-ls"><b>解</b></span>
              （3）
              观察图像可知，当<i>y</i>=0时，对应抛物线与<i>x</i>轴的两个交点，此时<i>x</i>有两个取值，<i>x</i><sub>1</sub>=-1，<i>x</i><sub>2</sub>=3；
            </p>
            <p>
              当<i>y</i>＞0时，对应抛物线在<i>x</i>轴上方的所有点，此时<i>x</i>的取值范围是<i>x</i>＜-1或<i>x</i>＞3；
            </p>
            <p>
              当<i>y</i>＜0时，对应抛物线在<i>x</i>轴下方的所有点，此时<i>x</i>的取值范围是-1＜<i>x</i>＜3.
            </p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
        </div>
      </div>
    </div>
@@ -1165,103 +1359,22 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0055-1.jpg" /></p>
          <p class="img">图2-3</p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1） 因为<i>a</i>=1＞0，所以函数图像为开口向上的抛物线.
          </p>
          <p>
            因为<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-2）<sup>2</sup>-4×1×（-3）=16＞0，
          </p>
          <p>
            所以一元二次方程<i>x</i><sup>2</sup>-2<i>x</i>-3=0有两个不相等的实数解.
          </p>
          <p>解方程，得<i>x</i><sub>1</sub>=-1，<i>x</i><sub>2</sub>=3.</p>
          <p>所以抛物线与<i>x</i>轴的交点坐标为（-1，0），（3，0）.</p>
          <p>
            抛物线的顶点坐标为<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
                <mfrac>
                  <mi>b</mi>
                  <mrow>
                    <mn>2</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
                <mo>，</mo>
                <mfrac>
                  <mrow>
                    <mn>4</mn>
                    <mi>a</mi>
                    <mi>c</mi>
                    <mo>−</mo>
                    <msup>
                      <mi>b</mi>
                      <mrow>
                        <mn>2</mn>
                      </mrow>
                    </msup>
                  </mrow>
                  <mrow>
                    <mn>4</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，即（1，-4）.
          </p>
          <p>
            抛物线的对称轴方程为<math display="0">
              <mi>x</mi>
              <mo>=</mo>
              <mo>−</mo>
              <mfrac>
                <mi>b</mi>
                <mrow>
                  <mn>2</mn>
                  <mi>a</mi>
                </mrow>
              </mfrac>
            </math>，即<i>x</i>=1.抛物线与<i>y</i>轴的交点坐标为（0，<i>c</i>），即（0，-3）.根据函数的对称性，可以再取一些点，如（2，-3）.
          </p>
          <p>
            根据以上信息，就可以画出函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3的图像（如图2-3所示）.
          </p>
          <p>
            （2）
            观察图像可知，满足<i>y</i>=0的点是抛物线与<i>x</i>轴的交点；满足<i>y</i>＞0的点是抛物线在<i>x</i>轴上方的所有点；满足<i>y</i>＜0的点是抛物线在<i>x</i>轴下方的所有点.
          </p>
          <p>
            （3）
            观察图像可知，当<i>y</i>=0时，对应抛物线与<i>x</i>轴的两个交点，此时<i>x</i>有两个取值，<i>x</i><sub>1</sub>=-1，<i>x</i><sub>2</sub>=3；
          </p>
          <p>
            当<i>y</i>＞0时，对应抛物线在<i>x</i>轴上方的所有点，此时<i>x</i>的取值范围是<i>x</i>＜-1或<i>x</i>＞3；
          </p>
          <p>
            当<i>y</i>＜0时，对应抛物线在<i>x</i>轴下方的所有点，此时<i>x</i>的取值范围是-1＜<i>x</i>＜3.
          </p>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[51] ? questionData[51][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
            <examinations :cardList="questionData[51] ? questionData[51][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <p>已知下列二次函数：</p>
            <p>①<i>y</i>=<i>x</i><sup>2</sup>-3<i>x</i>-4， ②<i>y</i>=<i>x</i><sup>2</sup>+<i>x</i>+2， ③<i>y</i>=<i>x</i><sup>2</sup>-6<i>x</i>+9.</p>
            <p>①<i>y</i>=<i>x</i><sup>2</sup>-3<i>x</i>-4， ②<i>y</i>=<i>x</i><sup>2</sup>+<i>x</i>+2，
              ③<i>y</i>=<i>x</i><sup>2</sup>-6<i>x</i>+9.</p>
            <p>（1） 分别画出它们的函数图像；</p>
            <paint 
              :page="51"
              :imgUrl="this.config.activeBook.resourceUrl + '/images/a6fe3d63.png'" 
            />
            <paint :page="51" :imgUrl="this.config.activeBook.resourceUrl + '/images/a6fe3d63.png'" />
            <p>
              （2） 根据函数图像写出<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0时所对应的<i>x</i>的值或取值范围.
              <span class="btn-box" @click="isShowAnswer = !isShowAnswer">
@@ -1272,23 +1385,334 @@
                </svg>
              </span>
            </p>
            <el-input type="textarea"  placeholder="请输入内容" rows="6" class="question-textarea" ></el-input>
            <el-input type="textarea" placeholder="请输入内容" rows="6" class="question-textarea"></el-input>
            <ul class="table-answer-box" v-if="isShowAnswer">
              <li>答案：</li>
              <li>
                <math  display="block">  <mrow>    <mo>&#x2460;</mo>  </mrow>  <mi>y</mi>  <mo>=</mo>  <msup>    <mi>x</mi>    <mrow>      <mn>2</mn>    </mrow>  </msup>  <mo>&#x2212;</mo>  <mn>3</mn>  <mi>x</mi>  <mo>&#x2212;</mo>  <mn>4</mn>  <mo>=</mo>  <mo stretchy="false">(</mo>  <mi>x</mi>  <mo>+</mo>  <mn>1</mn>  <mo stretchy="false">)</mo>  <mo stretchy="false">(</mo>  <mi>x</mi>  <mo>&#x2212;</mo>  <mn>4</mn>  <mo stretchy="false">)</mo></math>
                <math  display="block">  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>=</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>1</mn>    </mrow>  </msub>  <mo>=</mo>  <mo>&#x2212;</mo>  <mn>1</mn>  <mo>&#x6216;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>2</mn>    </mrow>  </msub>  <mo>=</mo>  <mn>4</mn>  <mo>&#xFF0C;</mo></math>
                <math  display="block">  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>&gt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;</mo>  <mi>x</mi>  <mo>&lt;</mo>  <mo>&#x2212;</mo>  <mn>1</mn>  <mo>&#x6216;</mo>  <mi>x</mi>  <mo>&gt;</mo>  <mn>4</mn>  <mo>&#xFF0C;</mo></math>
                <math  display="block">  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>&lt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;</mo>  <mo>&#x2212;</mo>  <mn>1</mn>  <mo>&lt;</mo>  <mi>x</mi>  <mo>&lt;</mo>  <mn>4</mn>  <mo>&#xFF1B;</mo></math>
                <math  display="block">  <mo>&#x56E0;&#x6B64;&#x5F53;</mo>  <mi>y</mi>  <mo>=</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>  <mo stretchy="false">(</mo>  <mo>&#x2212;</mo>  <mn>1</mn>  <mo>,</mo>  <mn>0</mn>  <mo stretchy="false">)</mo>  <mo>,</mo>  <mo stretchy="false">(</mo>  <mn>4</mn>  <mo>,</mo>  <mn>0</mn>  <mo stretchy="false">)</mo>  <mo>;</mo>  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>&gt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>  </math>
                <math  display="block"> <mo stretchy="false">(</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>,</mo>  <mi>y</mi>  <mo stretchy="false">)</mo>  <mo>&#xFF0C;&#x5176;&#x4E2D;&#xFF0C;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>&lt;</mo>  <mo>&#x2212;</mo>  <mn>1</mn>  <mo>&#x6216;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>&gt;</mo>  <mn>4</mn>  <mo>&#xFF1B;</mo> </math>
                <math  display="block">  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>&lt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>  <mo stretchy="false">(</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>,</mo>  <mi>y</mi>  <mo stretchy="false">)</mo>  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>  <mo>&#x2212;</mo>  <mn>1</mn>  <mo>&lt;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>&lt;</mo>  <mn>4</mn>  <mo>&#xFF1B;</mo></math>
                <math  display="block">  <mrow>    <mo>&#x2461;</mo>  </mrow>  <mi>y</mi>  <mo>=</mo>  <msup>    <mi>x</mi>    <mrow>      <mn>2</mn>    </mrow>  </msup>  <mo>+</mo>  <mi>x</mi>  <mo>+</mo>  <mn>2</mn>  <mo>=</mo>  <mo stretchy="false">(</mo>  <mi>x</mi>  <mo>+</mo>  <mfrac>    <mn>1</mn>    <mn>2</mn>  </mfrac>  <msup>    <mo stretchy="false">)</mo>    <mrow>      <mn>2</mn>    </mrow>  </msup>  <mo>+</mo>  <mfrac>    <mn>7</mn>    <mn>4</mn>  </mfrac>  <mo>&gt;</mo>  <mn>0</mn>  <mo>&#xFF1B;</mo></math>
                <math  display="block">  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>=</mo>  <mn>0</mn>  <mo>&#xFF0C;</mo>  <mi>y</mi>  <mo>&lt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6CA1;&#x6709;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#xFF1B;&#x5F53;</mo>  <mi>y</mi>  <mo>&gt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>  <mo stretchy="false">(</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>,</mo>  <mi>y</mi>  <mo stretchy="false">)</mo> </math>
                <math> <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>&#x2208;</mo>  <mi>R</mi>  <mo>.</mo></math>
                <math  display="block">  <mrow>    <mo>&#x2462;</mo>  </mrow>  <mi>y</mi>  <mo>=</mo>  <msup>    <mi>x</mi>    <mrow>      <mn>2</mn>    </mrow>  </msup>  <mo>&#x2212;</mo>  <mn>6</mn>  <mi>x</mi>  <mo>+</mo>  <mn>9</mn>  <mo>=</mo>  <mo stretchy="false">(</mo>  <mi>x</mi>  <mo>&#x2212;</mo>  <mn>3</mn>  <msup>    <mo stretchy="false">)</mo>    <mrow>      <mn>2</mn>    </mrow>  </msup>  <mo>.</mo></math>
                <math  display="block">  <mo>&#x5F53;</mo>  <mi>y</mi>  <mo>=</mo>  <mn>0</mn>  <mo>&#x65F6;</mo>  <mo>,</mo>  <mo>&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>  <mo stretchy="false">(</mo>  <mn>3</mn>  <mo>,</mo>  <mn>0</mn>  <mo stretchy="false">)</mo>  <mo>&#xFF1B;&#x5F53;</mo>  <mi>y</mi>  <mo>&gt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>  <mo stretchy="false">(</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>,</mo>  <mi>y</mi>  <mo stretchy="false">)</mo> </math>
                <math  display="block"> <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>  <msub>    <mi>x</mi>    <mrow>      <mn>0</mn>    </mrow>  </msub>  <mo>&#x2260;</mo>  <mn>3</mn>  <mo>&#xFF1B;&#x5F53;</mo>  <mi>y</mi>  <mo>&lt;</mo>  <mn>0</mn>  <mo>&#x65F6;&#xFF0C;&#x6CA1;&#x6709;&#x5BF9;&#x5E94;&#x7684;&#x70B9;</mo>  <mo>.</mo></math>
                <math display="block">
                  <mrow>
                    <mo>&#x2460;</mo>
                  </mrow>
                  <mi>y</mi>
                  <mo>=</mo>
                  <msup>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>&#x2212;</mo>
                  <mn>3</mn>
                  <mi>x</mi>
                  <mo>&#x2212;</mo>
                  <mn>4</mn>
                  <mo>=</mo>
                  <mo stretchy="false">(</mo>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>1</mn>
                  <mo stretchy="false">)</mo>
                  <mo stretchy="false">(</mo>
                  <mi>x</mi>
                  <mo>&#x2212;</mo>
                  <mn>4</mn>
                  <mo stretchy="false">)</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>=</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                  </msub>
                  <mo>=</mo>
                  <mo>&#x2212;</mo>
                  <mn>1</mn>
                  <mo>&#x6216;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msub>
                  <mo>=</mo>
                  <mn>4</mn>
                  <mo>&#xFF0C;</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&gt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;</mo>
                  <mi>x</mi>
                  <mo>&lt;</mo>
                  <mo>&#x2212;</mo>
                  <mn>1</mn>
                  <mo>&#x6216;</mo>
                  <mi>x</mi>
                  <mo>&gt;</mo>
                  <mn>4</mn>
                  <mo>&#xFF0C;</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&lt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;</mo>
                  <mo>&#x2212;</mo>
                  <mn>1</mn>
                  <mo>&lt;</mo>
                  <mi>x</mi>
                  <mo>&lt;</mo>
                  <mn>4</mn>
                  <mo>&#xFF1B;</mo>
                </math>
                <math display="block">
                  <mo>&#x56E0;&#x6B64;&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>=</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
                  <mo>&#x2212;</mo>
                  <mn>1</mn>
                  <mo>,</mo>
                  <mn>0</mn>
                  <mo stretchy="false">)</mo>
                  <mo>,</mo>
                  <mo stretchy="false">(</mo>
                  <mn>4</mn>
                  <mo>,</mo>
                  <mn>0</mn>
                  <mo stretchy="false">)</mo>
                  <mo>;</mo>
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&gt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                </math>
                <math display="block">
                  <mo stretchy="false">(</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>,</mo>
                  <mi>y</mi>
                  <mo stretchy="false">)</mo>
                  <mo>&#xFF0C;&#x5176;&#x4E2D;&#xFF0C;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>&lt;</mo>
                  <mo>&#x2212;</mo>
                  <mn>1</mn>
                  <mo>&#x6216;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>&gt;</mo>
                  <mn>4</mn>
                  <mo>&#xFF1B;</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&lt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>,</mo>
                  <mi>y</mi>
                  <mo stretchy="false">)</mo>
                  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>
                  <mo>&#x2212;</mo>
                  <mn>1</mn>
                  <mo>&lt;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>&lt;</mo>
                  <mn>4</mn>
                  <mo>&#xFF1B;</mo>
                </math>
                <math display="block">
                  <mrow>
                    <mo>&#x2461;</mo>
                  </mrow>
                  <mi>y</mi>
                  <mo>=</mo>
                  <msup>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>+</mo>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>2</mn>
                  <mo>=</mo>
                  <mo stretchy="false">(</mo>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mn>2</mn>
                  </mfrac>
                  <msup>
                    <mo stretchy="false">)</mo>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>+</mo>
                  <mfrac>
                    <mn>7</mn>
                    <mn>4</mn>
                  </mfrac>
                  <mo>&gt;</mo>
                  <mn>0</mn>
                  <mo>&#xFF1B;</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>=</mo>
                  <mn>0</mn>
                  <mo>&#xFF0C;</mo>
                  <mi>y</mi>
                  <mo>&lt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6CA1;&#x6709;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#xFF1B;&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&gt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>,</mo>
                  <mi>y</mi>
                  <mo stretchy="false">)</mo>
                </math>
                <math>
                  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>&#x2208;</mo>
                  <mi>R</mi>
                  <mo>.</mo>
                </math>
                <math display="block">
                  <mrow>
                    <mo>&#x2462;</mo>
                  </mrow>
                  <mi>y</mi>
                  <mo>=</mo>
                  <msup>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>&#x2212;</mo>
                  <mn>6</mn>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>9</mn>
                  <mo>=</mo>
                  <mo stretchy="false">(</mo>
                  <mi>x</mi>
                  <mo>&#x2212;</mo>
                  <mn>3</mn>
                  <msup>
                    <mo stretchy="false">)</mo>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>.</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>=</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;</mo>
                  <mo>,</mo>
                  <mo>&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
                  <mn>3</mn>
                  <mo>,</mo>
                  <mn>0</mn>
                  <mo stretchy="false">)</mo>
                  <mo>&#xFF1B;&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&gt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>,</mo>
                  <mi>y</mi>
                  <mo stretchy="false">)</mo>
                </math>
                <math display="block">
                  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>&#x2260;</mo>
                  <mn>3</mn>
                  <mo>&#xFF1B;&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&lt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6CA1;&#x6709;&#x5BF9;&#x5E94;&#x7684;&#x70B9;</mo>
                  <mo>.</mo>
                </math>
              </li>
            </ul>
          </div>
@@ -1502,34 +1926,57 @@
            上面的情形表明，二次函数图像的开口方向及其与<i>x</i>轴的交点坐标，可以确定其对应的一元二次不等式的解集.
          </p>
          <p><b>例</b> 利用二次函数的图像解下列一元二次不等式.</p>
          <p>
            （1） -<i>x</i><sup>2</sup>+3<i>x</i>+4＜0；（2） <i>x</i><sup>2</sup>-2<i>x</i>+3＞0.
          <p class="p-btn" >
            <span>（1） -<i>x</i><sup>2</sup>+3<i>x</i>+4＜0；</span>
            <span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0057-1.jpg" /></p>
          <p class="img">图2-5</p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            Δ=<i>b</i><sup>2</sup>-4<i>ac</i>=3<sup>2</sup>-4×（-1）×4=25＞0，所以函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像与<i>x</i>轴有两个交点.解方程-<i>x</i><sup>2</sup>+3<i>x</i>+4=0可得，<i>x</i>1=-1，<i>x</i>2=4.
          <div v-if="isShowAnswer12" >
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0057-1.jpg" /></p>
            <p class="img">图2-5</p>
            <p>
              <span class="zt-ls"><b>解</b></span>（1）
              Δ=<i>b</i><sup>2</sup>-4<i>ac</i>=3<sup>2</sup>-4×（-1）×4=25＞0，所以函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像与<i>x</i>轴有两个交点.解方程-<i>x</i><sup>2</sup>+3<i>x</i>+4=0可得，<i>x</i>1=-1，<i>x</i>2=4.
            </p>
            <p>
              函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像是开口向下的抛物线，与<i>x</i>轴的交点坐标是（-1，0），（4，0），函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像如图2-5所示.
            </p>
          </div>
          <p class="p-btn" >
            <span>（2） <i>x</i><sup>2</sup>-2<i>x</i>+3＞0.</span>
            <span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像是开口向下的抛物线，与<i>x</i>轴的交点坐标是（-1，0），（4，0），函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像如图2-5所示.
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0057-2.jpg" /></p>
          <p class="img">图2-6</p>
          <p>
            观察图像可得，不等式-<i>x</i><sup>2</sup>+3<i>x</i>+4＜0的解集是（-∞，
            -1）∪（4， +∞）.
          </p>
          <p>
            （2）
            <i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-2）<sup>2</sup>-4×1×3=-8＜0，所以函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>+3的图像与<i>x</i>轴无交点.
          </p>
          <p>
            函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>+3的图像是开口向上的抛物线，与<i>x</i>轴无交点，其简图如图2-6所示.
          </p>
          <p>
            观察图像可得，不等式<i>x</i><sup>2</sup>-2<i>x</i>+3＞0的解集为<b>R</b>.
          </p>
          <div v-if="isShowAnswer13" >
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0057-2.jpg" /></p>
            <p class="img">图2-6</p>
            <p>
              <span class="zt-ls"><b>解</b></span>
              观察图像可得，不等式-<i>x</i><sup>2</sup>+3<i>x</i>+4＜0的解集是（-∞，
              -1）∪（4， +∞）.
            </p>
            <p>
              （2）
              <i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-2）<sup>2</sup>-4×1×3=-8＜0，所以函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>+3的图像与<i>x</i>轴无交点.
            </p>
            <p>
              函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>+3的图像是开口向上的抛物线，与<i>x</i>轴无交点，其简图如图2-6所示.
            </p>
            <p>
              观察图像可得，不等式<i>x</i><sup>2</sup>-2<i>x</i>+3＞0的解集为<b>R</b>.
            </p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div class="bk">
            <div class="bj1">
              <p class="left">
@@ -1570,7 +2017,8 @@
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[54] ? questionData[54][1] : []" :hideCollect="true" sourceType="json" v-if="questionData">
            <examinations :cardList="questionData[54] ? questionData[54][1] : []" :hideCollect="true" sourceType="json"
              v-if="questionData">
            </examinations>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
@@ -1585,8 +2033,8 @@
          </p>
          <p>第三步：观察简图，写出不等式的解集.</p>
          <div class="bj">
            <examinations :cardList="questionData[54] ? questionData[54][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
            <examinations :cardList="questionData[54] ? questionData[54][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
        </div>
      </div>
@@ -1752,46 +2200,95 @@
          <p>
            <span class="zt-ls"><b>例1</b></span>　解下列不等式.
          </p>
          <p>
            （1）（<i>x</i>+3）（<i>x</i>+1）＜0；（2）（6-<i>x</i>）（<i>x</i>+4）≤0.
          <p class="p-btn" >
            <span>（1）（<i>x</i>+3）（<i>x</i>+1）＜0；</span>
            <span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1）（<i>x</i>+3）（<i>x</i>+1）＜0，即［<i>x</i>-（-3）］［<i>x</i>-（-1）］＜0.
          <div v-if="isShowAnswer14" >
            <p >
              <span class="zt-ls"><b>解</b></span>（1）（<i>x</i>+3）（<i>x</i>+1）＜0，即［<i>x</i>-（-3）］［<i>x</i>-（-1）］＜0.
            </p>
            <p >所以不等式的解集为（-3，-1）.</p>
          </div>
          <p class="p-btn" >
            <span>（2）（6-<i>x</i>）（<i>x</i>+4）≤0.</span>
            <span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>所以不等式的解集为（-3，-1）.</p>
          <p>
          <div v-if="isShowAnswer15" >
            <p>
              <span class="zt-ls"><b>解</b></span>
            （2）
            由（6-<i>x</i>）（<i>x</i>+4）≤0得（<i>x</i>-6）（<i>x</i>+4）≥0，即
              由（6-<i>x</i>）（<i>x</i>+4）≤0得（<i>x</i>-6）（<i>x</i>+4）≥0，即
            </p>
            <p class="center">（<i>x</i>-6）［<i>x</i>-（-4）］≥0.</p>
            <p>所以不等式的解集为（-∞，-4］∪［6，+∞）.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例2</b></span>　解下列不等式.
            </span>
            <span class="btn-box" @click="openDialog(thinkTwo)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="center">（<i>x</i>-6）［<i>x</i>-（-4）］≥0.</p>
          <p>所以不等式的解集为（-∞，-4］∪［6，+∞）.</p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　解下列不等式.
          <p class="p-btn" >
            <span>（1）（<i>x</i>+1）<sup>2</sup>≥4；</span>
            <span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            （1）（<i>x</i>+1）<sup>2</sup>≥4；（2）（2<i>x</i>-3）<sup>2</sup>＜9.
          <div v-if="isShowAnswer16" >
            <p>
              <span class="zt-ls"><b>解</b></span>（1）
              由（<i>x</i>+1）<sup>2</sup>≥4得（<i>x</i>+1）<sup>2</sup>-2<sup>2</sup>≥0，
            </p>
            <p>从而　　［（<i>x</i>+1）+2］［（<i>x</i>+1）-2］≥0，</p>
            <p>化简得（<i>x</i>+3）（<i>x</i>-1）≥0，</p>
            <p>即　　　［<i>x</i>-（-3）］（<i>x</i>-1）≥0，</p>
            <p>所以不等式的解集为（-∞，-3］∪［1，+∞）.</p>
          </div>
          <p class="p-btn" >
            <span>（2）（2<i>x</i>-3）<sup>2</sup>＜9.</span>
            <span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span
              class="zt-ls2"><b>分析</b></span>　由（<i>x</i>+1）<sup>2</sup>≥4得<i>x</i><sup>2</sup>+2<i>x</i>+1≥4，即<i>x</i><sup>2</sup>+2<i>x</i>-3≥0，从而可以利用二次函数<i>y</i>=<i>x</i><sup>2</sup>+2<i>x</i>-3的图像进行求解；注意到4=2<sup>2</sup>，也可以考虑将（<i>x</i>+1）<sup>2</sup>≥4整理为（<i>x</i>+1）<sup>2</sup>-4≥0，并使用平方差公式，即（<i>x</i>+1）<sup>2</sup>-2<sup>2</sup>≥0，得到（<i>x</i>+3）（<i>x</i>-1）≥0，此时可以借助上面的结论直接求解.下面我们将使用后一种方法进行求解.
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>（1）
            由（<i>x</i>+1）<sup>2</sup>≥4得（<i>x</i>+1）<sup>2</sup>-2<sup>2</sup>≥0，
          </p>
          <p>从而　　［（<i>x</i>+1）+2］［（<i>x</i>+1）-2］≥0，</p>
          <p>化简得（<i>x</i>+3）（<i>x</i>-1）≥0，</p>
          <p>即　　　［<i>x</i>-（-3）］（<i>x</i>-1）≥0，</p>
          <p>所以不等式的解集为（-∞，-3］∪［1，+∞）.</p>
          <p>
            （2）
            由（2<i>x</i>-3）<sup>2</sup>＜9得（2<i>x</i>-3）<sup>2</sup>-3<sup>2</sup>＜0，
          </p>
          <p>从而　　［（2<i>x</i>-3）+3］［（2<i>x</i>-3）-3］＜0，</p>
          <p>化简得　2<i>x</i>（2<i>x</i>-6）＜0，</p>
          <p>即　　　<i>x</i>（<i>x</i>-3）＜0，</p>
          <p>即（<i>x</i>-0）（<i>x</i>-3）＜0，</p>
          <p>所以不等式的解集为（0，3）.</p>
          <div v-if="isShowAnswer17" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              （2）
              由（2<i>x</i>-3）<sup>2</sup>＜9得（2<i>x</i>-3）<sup>2</sup>-3<sup>2</sup>＜0，
            </p>
            <p>从而　　［（2<i>x</i>-3）+3］［（2<i>x</i>-3）-3］＜0，</p>
            <p>化简得　2<i>x</i>（2<i>x</i>-6）＜0，</p>
            <p>即　　　<i>x</i>（<i>x</i>-3）＜0，</p>
            <p>即（<i>x</i>-0）（<i>x</i>-3）＜0，</p>
            <p>所以不等式的解集为（0，3）.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <p>解下列一元二次不等式.</p>
@@ -2060,60 +2557,73 @@
          </li>
        </ul>
        <div class="padding-116">
          <p><b>例</b> 解不等式|2<i>x</i>|＜5.</p>
          <p>
            <span class="zt-ls"><b>解</b></span>
            由|2<i>x</i>|＜5得-5＜2<i>x</i>＜5，
          <p class="p-btn" >
            <span>
              <b>例</b> 解不等式|2<i>x</i>|＜5.
            </span>
            <span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            即　<math display="0">
              <mo>−</mo>
              <mfrac>
                <mn>5</mn>
                <mn>2</mn>
              </mfrac>
              <mo>＜</mo>
              <mi>x</mi>
              <mo>＜</mo>
              <mfrac>
                <mn>5</mn>
                <mn>2</mn>
              </mfrac>
            </math>.
          </p>
          <p>
            所以不等式的解集是<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
          <div v-if="isShowAnswer18" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|2<i>x</i>|＜5得-5＜2<i>x</i>＜5，
            </p>
            <p>
              即　<math display="0">
                <mo>−</mo>
                <mfrac>
                  <mn>5</mn>
                  <mn>2</mn>
                </mfrac>
                <mo>，</mo>
                <mo>＜</mo>
                <mi>x</mi>
                <mo>＜</mo>
                <mfrac>
                  <mn>5</mn>
                  <mn>2</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>.
          </p>
              </math>.
            </p>
            <p>
              所以不等式的解集是<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>5</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo>，</mo>
                  <mfrac>
                    <mn>5</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[60] ? questionData[60][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
            v-if="questionData"></examinations>
            <examinations :cardList="questionData[60] ? questionData[60][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
          <div class="bj">
            <examinations :cardList="questionData[60] ? questionData[60][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
            v-if="questionData"></examinations>
            <examinations :cardList="questionData[60] ? questionData[60][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h3 id="c021">
            2.4.2
@@ -2123,23 +2633,49 @@
          <p>
            求解此类不等式时，可以将<i>ax</i>+<i>b</i>看作一个整体，再利用含绝对值不等式的基本解法，去掉绝对值，然后进行求解.
          </p>
          <p>
            <span class="zt-ls"><b>例1</b></span>　解不等式|2<i>x</i>-1|＜5.
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例1</b></span>　解不等式|2<i>x</i>-1|＜5.
            </span>
            <span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>
            由|2<i>x</i>-1|＜5得-5＜2<i>x</i>-1＜5，
          <div v-if="isShowAnswer19" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|2<i>x</i>-1|＜5得-5＜2<i>x</i>-1＜5，
            </p>
            <p>即　-4＜2<i>x</i>＜6，</p>
            <p>　　-2＜<i>x</i>＜3.</p>
            <p>所以不等式的解集是（-2，3）.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例2</b></span>　解不等式|1-2<i>x</i>|＜3.
            </span>
            <span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>即　-4＜2<i>x</i>＜6，</p>
          <p>　　-2＜<i>x</i>＜3.</p>
          <p>所以不等式的解集是（-2，3）.</p>
          <p>
            <span class="zt-ls"><b>例2</b></span>　解不等式|1-2<i>x</i>|＜3.
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span> 因为|1-2<i>x</i>|=|2<i>x</i>-1|，
          </p>
          <p>所以由|1-2<i>x</i>|＜3得|2<i>x</i>-1|＜3.</p>
          <div v-if="isShowAnswer20" >
            <p>
              <span class="zt-ls"><b>解</b></span> 因为|1-2<i>x</i>|=|2<i>x</i>-1|，
            </p>
            <p>所以由|1-2<i>x</i>|＜3得|2<i>x</i>-1|＜3.</p>
            <p>由|2<i>x</i>-1|＜3得-3＜2<i>x</i>-1＜3，</p>
            <p>即　-2＜2<i>x</i>＜4，</p>
            <p>　　-1＜<i>x</i>＜2.</p>
            <p>所以不等式的解集是（-1，2）.</p>
          </div>
        </div>
      </div>
    </div>
@@ -2152,38 +2688,56 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>由|2<i>x</i>-1|＜3得-3＜2<i>x</i>-1＜3，</p>
          <p>即　-2＜2<i>x</i>＜4，</p>
          <p>　　-1＜<i>x</i>＜2.</p>
          <p>所以不等式的解集是（-1，2）.</p>
          <p>
            <span class="zt-ls"><b>例3</b></span>　解不等式|<i>x</i>+3|≥2.
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例3</b></span>　解不等式|<i>x</i>+3|≥2.
            </span>
            <span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>
            由|<i>x</i>+3|≥2得<i>x</i>+3≤-2或<i>x</i>+3≥2，
          <div v-if="isShowAnswer21" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|<i>x</i>+3|≥2得<i>x</i>+3≤-2或<i>x</i>+3≥2，
            </p>
            <p>即　<i>x</i>≤-5或<i>x</i>≥-1.</p>
            <p>所以不等式的解集是（-∞，-5］∪［-1，+∞）.</p>
            <p>
              现在我们回到本节开始的问题，解不等式|<i>x</i>-100|≤3得97≤<i>x</i>≤103，解不等式|<i>x</i>-100|＞3得<i>x</i>＞103或<i>x</i>＜97.如果产权登记面积在97
              m<sup>2</sup>和103 m<sup>2</sup>之间（包含97 m<sup>2</sup>和103
              m<sup>2</sup>）
              时，李先生按照产权登记面积结算房款；如果产权登记面积小于97
              m<sup>2</sup>或大于103 m<sup>2</sup>时，李先生有权退房.
            </p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例4</b></span>　解不等式|3<i>x</i>-（<i>x</i>-2）|≤2.
            </span>
            <span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>即　<i>x</i>≤-5或<i>x</i>≥-1.</p>
          <p>所以不等式的解集是（-∞，-5］∪［-1，+∞）.</p>
          <p>
            现在我们回到本节开始的问题，解不等式|<i>x</i>-100|≤3得97≤<i>x</i>≤103，解不等式|<i>x</i>-100|＞3得<i>x</i>＞103或<i>x</i>＜97.如果产权登记面积在97
            m<sup>2</sup>和103 m<sup>2</sup>之间（包含97 m<sup>2</sup>和103
            m<sup>2</sup>）
            时，李先生按照产权登记面积结算房款；如果产权登记面积小于97
            m<sup>2</sup>或大于103 m<sup>2</sup>时，李先生有权退房.
          </p>
          <p>
            <span class="zt-ls"><b>例4</b></span>　解不等式|3<i>x</i>-（<i>x</i>-2）|≤2.
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span>
            由|3<i>x</i>-（<i>x</i>-2）|≤2得|3<i>x</i>-<i>x</i>+2|≤2，
          </p>
          <p>即　　|2<i>x</i>+2|≤2，</p>
          <p>从而　-2≤2<i>x</i>+2≤2，</p>
          <p>　　　-4≤2<i>x</i>≤0，</p>
          <p>　　　-2≤<i>x</i>≤0.</p>
          <p>所以不等式的解集是［-2，0］.</p>
          <div v-if="isShowAnswer22">
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|3<i>x</i>-（<i>x</i>-2）|≤2得|3<i>x</i>-<i>x</i>+2|≤2，
            </p>
            <p>即　　|2<i>x</i>+2|≤2，</p>
            <p>从而　-2≤2<i>x</i>+2≤2，</p>
            <p>　　　-4≤2<i>x</i>≤0，</p>
            <p>　　　-2≤<i>x</i>≤0.</p>
            <p>所以不等式的解集是［-2，0］.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[61]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
@@ -2217,11 +2771,20 @@
          </h3>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0066-11.jpg" /></p>
          <p class="img">图2-12</p>
          <p>
            <span class="zt-ls"><b>例1</b></span>　用篱笆在墙边围一块矩形小花坛，其中一边靠墙（如图2-12所示），篱笆总长为8m.若小花坛的面积不小于6
            m<sup>2</sup>，则小花坛垂直于墙的一边的长度范围是多少？
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例1</b></span>　用篱笆在墙边围一块矩形小花坛，其中一边靠墙（如图2-12所示），篱笆总长为8m.若小花坛的面积不小于6
              m<sup>2</sup>，则小花坛垂直于墙的一边的长度范围是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
          <p v-if="isShowAnswer23" >
            <span class="zt-ls"><b>解</b></span>
            设小花坛垂直于墙的一边的长度为<i>x</i>（m），则与墙平行的一边的长度为（8-2<i>x</i>）m.考虑到实际情况，有<i>x</i>＞0，并且8-2<i>x</i>＞0，所以<i>x</i>满足0＜<i>x</i>＜4.
          </p>
@@ -2237,32 +2800,46 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>设小花坛的面积为<i>S</i>（m<sup>2</sup>），则</p>
          <p class="center"><i>S</i>=<i>x</i>（8-2<i>x</i>），</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0067-1.jpg" /></p>
          <p class="img">图2-13</p>
          <p>整理得 <i>S</i>=-2<i>x</i><sup>2</sup>+8<i>x</i>.</p>
          <p>
            由题意得 <i>S</i>=-2<i>x</i><sup>2</sup>+8<i>x</i>≥6，即<i>x</i><sup>2</sup>-4<i>x</i>+3≤0.
          </p>
          <p>
            画出二次函数<i>y</i>=<i>x</i><sup>2</sup>-4<i>x</i>+3的简图（如图2-13所示）.
          </p>
          <p>由图像得不等式的解为{<i>x</i>|1≤<i>x</i>≤3}.</p>
          <p>结合0＜<i>x</i>＜4，得</p>
          <p class="center">
            {<i>x</i>|0＜<i>x</i>＜4}∩{<i>x</i>|1≤<i>x</i>≤3}={<i>x</i>|1≤<i>x</i>≤3}.
          </p>
          <p>所以小花坛垂直于墙的一边的长度在1m至3m之间（含1m和3m）.</p>
          <p>
            <span
          <div v-if="isShowAnswer23">
            <p>设小花坛的面积为<i>S</i>（m<sup>2</sup>），则</p>
            <p class="center"><i>S</i>=<i>x</i>（8-2<i>x</i>），</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0067-1.jpg" /></p>
            <p class="img">图2-13</p>
            <p>整理得 <i>S</i>=-2<i>x</i><sup>2</sup>+8<i>x</i>.</p>
            <p>
              由题意得 <i>S</i>=-2<i>x</i><sup>2</sup>+8<i>x</i>≥6，即<i>x</i><sup>2</sup>-4<i>x</i>+3≤0.
            </p>
            <p>
              画出二次函数<i>y</i>=<i>x</i><sup>2</sup>-4<i>x</i>+3的简图（如图2-13所示）.
            </p>
            <p>由图像得不等式的解为{<i>x</i>|1≤<i>x</i>≤3}.</p>
            <p>结合0＜<i>x</i>＜4，得</p>
            <p class="center">
              {<i>x</i>|0＜<i>x</i>＜4}∩{<i>x</i>|1≤<i>x</i>≤3}={<i>x</i>|1≤<i>x</i>≤3}.
            </p>
            <p>所以小花坛垂直于墙的一边的长度在1m至3m之间（含1m和3m）.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例2</b></span>　某网店销售一种电动玩具，成本为10元/个.平时按单价20元销售，日平均销售量为100个.为进一步提升业绩，该网店决定在“双11”期间举办降价促销活动.根据以往的统计，如果该电动玩具的单价每降低0.5元，日平均销售量就会大约增加10个.为了使促销活动期间日平均利润不低于平时，应如何确定降价的范围？
            </span>
            <span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
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                  transform="translate(-3327.144 15329)" />
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            <span class="btn-box" @click="openDialog(thinkThree)">
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                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="block">
            <span
              class="zt-ls2"><b>分析</b></span>　利润=（销售单价-成本单价）×销售量.降价过程中，单价降低能够使销售量变大，但也使销售单价与成本单价的差减小，所以降价的范围应保证利润不低于促销前.
          </p>
          <div class="bk">
          <div class="bk mt-60" >
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
@@ -2272,32 +2849,34 @@
              由例1和例2可知，在解决与一元二次不等式有关的实际问题时，不仅要解一元二次不等式，而且要考虑实际背景对未知数的限制.在例1中，实际背景对未知数的限制是0＜<i>x</i>＜4；在例2中，实际背景对未知数的限制是0＜<i>x</i>＜10.
            </p>
          </div>
          <p>
            <span class="zt-ls"><b>解</b></span>
            假设降价<i>x</i>元.考虑到实际情况，价格的降幅应小于10元，即保证销售价高于成本价，所以要求<i>x</i>＞0并且<i>x</i>＜10，即0＜<i>x</i>＜10.
          </p>
          <p>平时的日平均利润为（20-10）×100=1 000（元）.</p>
          <p>
            降价<i>x</i>元后，销售单价为（20-<i>x</i>）元，单个玩具的利润为（20-<i>x</i>）-10=（10-<i>x</i>）元，日平均销售量为<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mn>100</mn>
                <mo>+</mo>
                <mfrac>
                  <mn>10</mn>
                  <mn>0.5</mn>
                </mfrac>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>个.因此，降价<i>x</i>元后的日平均利润为（10-<i>x</i>）（100+20<i>x</i>）元.
          </p>
          <p>由题意得（10-<i>x</i>）（100+20<i>x</i>）≥1 000.</p>
          <p>化简得<i>x</i><sup>2</sup>-5<i>x</i>≤0，即<i>x</i>（<i>x</i>-5）≤0.</p>
          <p>所以不等式的解集为 {<i>x</i>|0≤<i>x</i>≤5}.</p>
          <p>
            由于0＜<i>x</i>＜10，所以<i>x</i>的范围是{<i>x</i>|0＜<i>x</i>＜10}∩{<i>x</i>|0≤<i>x</i>≤5}，即{<i>x</i>|0＜<i>x</i>≤5}.所以降价的范围应在0至5元之间（含5元，不含0元），即单价定在15元至20元之间（含15元，不含20元），便能满足要求.
          </p>
          <div v-if="isShowAnswer24">
            <p>
              <span class="zt-ls"><b>解</b></span>
              假设降价<i>x</i>元.考虑到实际情况，价格的降幅应小于10元，即保证销售价高于成本价，所以要求<i>x</i>＞0并且<i>x</i>＜10，即0＜<i>x</i>＜10.
            </p>
            <p>平时的日平均利润为（20-10）×100=1 000（元）.</p>
            <p>
              降价<i>x</i>元后，销售单价为（20-<i>x</i>）元，单个玩具的利润为（20-<i>x</i>）-10=（10-<i>x</i>）元，日平均销售量为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mn>100</mn>
                  <mo>+</mo>
                  <mfrac>
                    <mn>10</mn>
                    <mn>0.5</mn>
                  </mfrac>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>个.因此，降价<i>x</i>元后的日平均利润为（10-<i>x</i>）（100+20<i>x</i>）元.
            </p>
            <p>由题意得（10-<i>x</i>）（100+20<i>x</i>）≥1 000.</p>
            <p>化简得<i>x</i><sup>2</sup>-5<i>x</i>≤0，即<i>x</i>（<i>x</i>-5）≤0.</p>
            <p>所以不等式的解集为 {<i>x</i>|0≤<i>x</i>≤5}.</p>
            <p>
              由于0＜<i>x</i>＜10，所以<i>x</i>的范围是{<i>x</i>|0＜<i>x</i>＜10}∩{<i>x</i>|0≤<i>x</i>≤5}，即{<i>x</i>|0＜<i>x</i>≤5}.所以降价的范围应在0至5元之间（含5元，不含0元），即单价定在15元至20元之间（含15元，不含20元），便能满足要求.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
@@ -2322,8 +2901,6 @@
          </li>
        </ul>
        <div class="padding-116">
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0068-1.jpg" /></p>
          <p class="img">第2题图</p>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[64]" :hideCollect="true" sourceType="json" v-if="questionData">
@@ -2332,31 +2909,43 @@
          <h3 id="c024">
            2.5.2 不等式与复杂实际问题<span class="fontsz2">＞＞＞</span>
          </h3>
          <p>
            <span
              class="zt-ls"><b>例1</b></span>　我国交通法规对小型汽车驾驶员的年龄限制如下：最低年龄18周岁，最高年龄70周岁.已有研究表明，小型汽车驾驶员对红绿灯变化的反应时间<i>y</i>（ms）
            与驾驶员年龄<i>x</i>（周岁）
            的关系为<i>y</i>=0.005<i>x</i><sup>2</sup>-0.2<i>x</i>+22，其中18≤<i>x</i>≤70.问：反应时间超过24.5ms的驾驶员所处的年龄范围是多少？
          <p class="p-btn" >
            <span>
              <span
                class="zt-ls"><b>例1</b></span>　我国交通法规对小型汽车驾驶员的年龄限制如下：最低年龄18周岁，最高年龄70周岁.已有研究表明，小型汽车驾驶员对红绿灯变化的反应时间<i>y</i>（ms）
              与驾驶员年龄<i>x</i>（周岁）
              的关系为<i>y</i>=0.005<i>x</i><sup>2</sup>-0.2<i>x</i>+22，其中18≤<i>x</i>≤70.问：反应时间超过24.5ms的驾驶员所处的年龄范围是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>
            <span class="zt-ls"><b>解</b></span> 由题意得，<i>y</i>=0.005<i>x</i><sup>2</sup>-0.2<i>x</i>+22＞24.5，即
          </p>
          <p>　　　　　0.005<i>x</i><sup>2</sup>-0.2<i>x</i>-2.5＞0.</p>
          <p>化简得 <i>x</i><sup>2</sup>-40<i>x</i>-500＞0.</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0068-2.jpg" /></p>
          <p class="img">图2-14</p>
          <p>
            考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>-500，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-40）<sup>2</sup>-4×1×（-500）=3
            600＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>-500的图像开口向上，并且与<i>x</i>轴有两个交点.其简图如图2-14所示.
          </p>
          <p>
            由图像可知，不等式<i>x</i><sup>2</sup>-40<i>x</i>-500＞0的解集为（-∞，-10）∪（50，+∞），这也是不等式0.005<i>x</i><sup>2</sup>-0.2<i>x</i>-2.5＞0的解集.
          </p>
          <p>
            考虑到18≤<i>x</i>≤70，所以<i>x</i>的范围是（50，70］，即反应时间超过24.5
            <i>ms</i>
            的驾驶员所处的年龄范围在50岁至70岁之间（不包含50岁，包含70岁）.
          </p>
          <div v-if="isShowAnswer25" >
            <p>
              <span class="zt-ls"><b>解</b></span> 由题意得，<i>y</i>=0.005<i>x</i><sup>2</sup>-0.2<i>x</i>+22＞24.5，即
            </p>
            <p>　　　　　0.005<i>x</i><sup>2</sup>-0.2<i>x</i>-2.5＞0.</p>
            <p>化简得 <i>x</i><sup>2</sup>-40<i>x</i>-500＞0.</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0068-2.jpg" /></p>
            <p class="img">图2-14</p>
            <p>
              考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>-500，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-40）<sup>2</sup>-4×1×（-500）=3
              600＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>-500的图像开口向上，并且与<i>x</i>轴有两个交点.其简图如图2-14所示.
            </p>
            <p>
              由图像可知，不等式<i>x</i><sup>2</sup>-40<i>x</i>-500＞0的解集为（-∞，-10）∪（50，+∞），这也是不等式0.005<i>x</i><sup>2</sup>-0.2<i>x</i>-2.5＞0的解集.
            </p>
            <p>
              考虑到18≤<i>x</i>≤70，所以<i>x</i>的范围是（50，70］，即反应时间超过24.5
              <i>ms</i>
              的驾驶员所处的年龄范围在50岁至70岁之间（不包含50岁，包含70岁）.
            </p>
          </div>

          <p>
            <span class="zt-ls"><b>例2</b></span>　身体质量指数（Body Mass
            Index，BMI）是衡量人体胖瘦程度的一个常用标准，计算公式为<math display="0">
@@ -2398,44 +2987,55 @@
            000m跑、女生800m跑），坐位体前屈等项目的成绩总和.身体素质指标为正数说明身体素质较好.上述研究发现，身体素质指标（<i>y</i>）与BMI（<i>x</i>）
            之间的关系如表2-7所示.
          </p>
          <p>问：身体素质较好的男生和女生，其BMI的范围分别是多少？</p>
          <p class="p-btn" >
            问：身体素质较好的男生和女生，其BMI的范围分别是多少？
            <span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">表2-7</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0069-1.jpg" /></p>
          <p>
            <span class="zt-ls"><b>解</b></span>
            先考虑男生的情况.由题意得，<i>y</i>=-0.05<i>x</i><sup>2</sup>+2<i>x</i>-19.2＞0，即
          </p>
          <p class="center">0.05<i>x</i><sup>2</sup>-2<i>x</i>+19.2＜0.</p>
          <p>化简得　<i>x</i><sup>2</sup>-40<i>x</i>+384＜0.</p>
          <p>
            考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>+384，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=40<sup>2</sup>-4×1×384=64＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>+384的图像开口向上，与<i>x</i>轴有两个交点.
          </p>
          <p>
            所以不等式<i>x</i><sup>2</sup>-40<i>x</i>+384＜0的解集为（16，24），这也是不等式-0.05<i>x</i><sup>2</sup>+2<i>x</i>-19.2＞0的解集.
          </p>
          <p>
            再考虑女生的情况.由题意得，<i>y</i>=-0.01<i>x</i><sup>2</sup>+0.39<i>x</i>-3.68＞0，即
          </p>
          <p class="center">0.01<i>x</i><sup>2</sup>-0.39<i>x</i>+3.68＜0.</p>
          <p>化简得　<i>x</i><sup>2</sup>-39<i>x</i>+368＜0.</p>
          <p>
            考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-39<i>x</i>+368，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-39）<sup>2</sup>-4×1×368=49＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-39<i>x</i>+368的图像开口向上，与<i>x</i>轴有两个交点.
          </p>
          <p>
            所以不等式<i>x</i><sup>2</sup>-39<i>x</i>+368＜0的解集为（16，23），这也是不等式-0.01<i>x</i><sup>2</sup>+0.39<i>x</i>-3.68＞0的解集.
          </p>
          <p>
            因此，身体素质较好的男生BMI 的范围是（16，24），身体素质较好的女生BMI
            的范围是（16，23）.
          </p>
          <div v-if="isShowAnswer26" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              先考虑男生的情况.由题意得，<i>y</i>=-0.05<i>x</i><sup>2</sup>+2<i>x</i>-19.2＞0，即
            </p>
            <p class="center">0.05<i>x</i><sup>2</sup>-2<i>x</i>+19.2＜0.</p>
            <p>化简得　<i>x</i><sup>2</sup>-40<i>x</i>+384＜0.</p>
            <p>
              考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>+384，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=40<sup>2</sup>-4×1×384=64＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>+384的图像开口向上，与<i>x</i>轴有两个交点.
            </p>
            <p>
              所以不等式<i>x</i><sup>2</sup>-40<i>x</i>+384＜0的解集为（16，24），这也是不等式-0.05<i>x</i><sup>2</sup>+2<i>x</i>-19.2＞0的解集.
            </p>
            <p>
              再考虑女生的情况.由题意得，<i>y</i>=-0.01<i>x</i><sup>2</sup>+0.39<i>x</i>-3.68＞0，即
            </p>
            <p class="center">0.01<i>x</i><sup>2</sup>-0.39<i>x</i>+3.68＜0.</p>
            <p>化简得　<i>x</i><sup>2</sup>-39<i>x</i>+368＜0.</p>
            <p>
              考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-39<i>x</i>+368，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-39）<sup>2</sup>-4×1×368=49＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-39<i>x</i>+368的图像开口向上，与<i>x</i>轴有两个交点.
            </p>
            <p>
              所以不等式<i>x</i><sup>2</sup>-39<i>x</i>+368＜0的解集为（16，23），这也是不等式-0.01<i>x</i><sup>2</sup>+0.39<i>x</i>-3.68＞0的解集.
            </p>
            <p>
              因此，身体素质较好的男生BMI 的范围是（16，24），身体素质较好的女生BMI
              的范围是（16，23）.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[65]" :hideCollect="true" sourceType="json"
            v-if="questionData" ></examinations>
            <examinations :cardList="questionData[65]" :hideCollect="true" sourceType="json" v-if="questionData">
            </examinations>
          </div>
        </div>
      </div>
@@ -2456,12 +3056,13 @@
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
          <div class="bj">
            <examinations :cardList="questionData[66] ? questionData[66][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
            <examinations :cardList="questionData[66] ? questionData[66][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h3 id="c025">习题2.5<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[66] ? questionData[66][2] : []" :hideCollect="true" sourceType="json" v-if="questionData">
            <examinations :cardList="questionData[66] ? questionData[66][2] : []" :hideCollect="true" sourceType="json"
              v-if="questionData">
            </examinations>
          </div>
        </div>
@@ -2994,10 +3595,67 @@
    <!-- 066 -->
    <div class="page-box hidePage" page="73">
    </div>
    <!-- 解题思路弹窗 -->
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
      @close="closeDialog" class="thinkDialog">
      <div slot="title" class="think-header"
        style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 分析 </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797" p-id="4253"></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797" p-id="4254"></path>
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in thinkData" :key="index">
          <div v-if="index <= showIndex" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
                v-if="index < thinkOne.length - 1" />
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p" v-html="item"></p>
          </div>
        </li>
      </ul>
      <div @click="changeNext" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
            d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
            fill="#1296db" p-id="5068" />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db" p-id="5069" />
        </svg>
      </div>
    </el-dialog>
  </div>
</template>

<script>
const handleShow = (num) => {
  const obj = {}
  for (let index = 0; index < num; index++) {
    obj['isShowAnswer' + index] = false
  }
  return obj
}
const showObj = handleShow(30)
import paint from '@/components/paint/index.vue'
import examinations from '@/components/examinations/index.vue'
export default {
@@ -3011,14 +3669,47 @@
      type: Object,
    },
  },
  components: { examinations,paint },
  components: { examinations, paint },
  data() {
    return {
      isShowAnswer:false
      collectImg: require('../../assets/images/icon/heart.png'),
      collectCheck: require('../../assets/images/icon/heart-check.png'),
      thinkingDialog: false,
      showIndex: 0,
      thinkData: [],
      thinkOne: [
        '①根据<i>x</i><sup>2</sup>的系数判断函数图像（抛物线）的开口方向；',
        '②用判别式判定出一元二次方程<i>x</i><sup>2</sup>-2<i>x</i>-3=0的解的情况，从而确定二次函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3的图像与<i>x</i>轴的交点个数和交点坐标；',
        '③计算二次函数图像的顶点坐标、与<i>y</i>轴的交点坐标；',
        '④求出二次函数图像的对称轴方程，并利用函数图像的对称性再找出一些点；⑤最后根据上述信息画出函数图像.',
        '画出图像后，<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0分别对应函数图像与<i>x</i>轴相交、函数图像在<i>x</i>轴上方、函数图像在<i>x</i>轴下方三种情形，根据图像完成（2）（3）两个问题.'
      ],
      thinkTwo:[
        '由（<i>x</i>+1）<sup>2</sup>≥4得<i>x</i><sup>2</sup>+2<i>x</i>+1≥4，即<i>x</i><sup>2</sup>+2<i>x</i>-3≥0，从而可以利用二次函数<i>y</i>=<i>x</i><sup>2</sup>+2<i>x</i>-3的图像进行求解；注意到4=2<sup>2</sup>，也可以考虑将（<i>x</i>+1）<sup>2</sup>≥4整理为（<i>x</i>+1）<sup>2</sup>-4≥0，并使用平方差公式，即（<i>x</i>+1）<sup>2</sup>-2<sup>2</sup>≥0，得到（<i>x</i>+3）（<i>x</i>-1）≥0，此时可以借助上面的结论直接求解.下面我们将使用后一种方法进行求解.'
      ],
      thinkThree:[
        '利润=（销售单价-成本单价）×销售量.降价过程中，单价降低能够使销售量变大，但也使销售单价与成本单价的差减小，所以降价的范围应保证利润不低于促销前.'
      ],
      isShowAnswer: false,
      isShowAnswerOne: false,
      ...showObj
    };
  },
  mounted() { },
  methods: {},
  mounted() {
    console.log(2, this);
  },
  methods: {
    openDialog(queryData) {
      this.thinkData = queryData
      this.thinkingDialog = !this.thinkingDialog
    },
    closeDialog() {
      this.showIndex = 0
    },
    changeNext() {
      if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
    }
  },
};
</script>

@@ -3033,15 +3724,21 @@
  top: 0;
  width: 140px;
}

.question-textarea {
  margin-left: 20px;
  width: 94%;
  border-color:#DCDFE6;
  border-color: #DCDFE6;
}

.table-answer-box {
  math {
    width: max-content;
    height: 36px;
  }
}

li {
  list-style: none;
}
</style>

 src/books/mathBook/view/components/chapter003.vue

@@ -1,5 +1,5 @@
<template>
  <div class="chapter" num="3">
  <div class="chapter" num="4">
    <!-- 第三单元首页 -->
    <div class="page-box" page="74">
      <div v-if="showPageList.indexOf(74) > -1">
@@ -124,21 +124,45 @@
          </li>
        </ul>
        <div class="padding-116">
          <p><span
              class="zt-ls"><b>例1</b></span>　我国要建设现代化产业体系，推动制造业高端化发展.李平制作了6个机械零件，它们的直径如表3-2所示.请用函数的概念描述李平制作这批机械零件的直径<i>y</i>（<i>mm</i>
            ）与零件的标号<i>x</i>的函数关系.</p>
          <p class="p-btn" >
            <span>
              <span
                class="zt-ls"><b>例1</b></span>　我国要建设现代化产业体系，推动制造业高端化发展.李平制作了6个机械零件，它们的直径如表3-2所示.请用函数的概念描述李平制作这批机械零件的直径<i>y</i>（<i>mm</i>
              ）与零件的标号<i>x</i>的函数关系.
            </span>
            <span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">表3-2</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0082-1.jpg" /></p>
          <p><span class="zt-ls"><b>解</b></span>
          <p v-if="isShowAnswer0" >
            <span class="zt-ls"><b>解</b></span>
            设<i>x</i>表示零件的标号，<i>y</i>表示零件的直径，由表3-2，{1，2，3，4，5，6}中的任一数，<i>y</i>都有任一确定的值与它对应，所以表3-2确定了<i>y</i>与<i>x</i>的函数关系，其定义域为{1，2，3，4，5，6}，值域为{13.40，13.50，13.55，13.60，13.65，13.70}.
          </p>
          <p><span
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例2</b></span>　已知函数<i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>-1.当自变量<i>x</i>为-1，0，1，<i>a</i>时，求它们所对应的函数值.
            </span>
            <span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>解</b></span> <i>f</i>（-1）=3×（-1）<sup>2</sup>-1=3-1=2，</p>
          <p>　 <i>f</i>（0）=3×0<sup>2</sup>-1=0-1=-1，</p>
          <p>　 <i>f</i>（1）=3×1<sup>2</sup>-1=3-1=2，</p>
          <p>　 <i>f</i>（<i>a</i>）=3×<i>a</i><sup>2</sup>-1=3<i>a</i><sup>2</sup>-1.</p>
          <div v-if="isShowAnswer1" >
            <p><span class="zt-ls"><b>解</b></span> <i>f</i>（-1）=3×（-1）<sup>2</sup>-1=3-1=2，</p>
            <p>　 <i>f</i>（0）=3×0<sup>2</sup>-1=0-1=-1，</p>
            <p>　 <i>f</i>（1）=3×1<sup>2</sup>-1=3-1=2，</p>
            <p>　 <i>f</i>（<i>a</i>）=3×<i>a</i><sup>2</sup>-1=3<i>a</i><sup>2</sup>-1.</p>
          </div>    
          <div class="fieldset">
            <p><b>相关链接</b></p>
            <p class="block">魔方是由6个不同颜色的面组成的正方体，它可组成约4 325亿亿种不同颜色的组合，其最佳复原魔方颜色组合的方法是用数学方法研究出来的.</p>
@@ -154,11 +178,24 @@
          </div>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0082-2.jpg" /></p>
          <p class="img">图3-2</p>
          <p><span class="zt-ls"><b>例3</b></span>　如图3-2所示，一个边长是<i>a</i>的正方体，体积是<i>V</i>，写出体积<i>V</i> 随边长<i>a</i>
            变化的函数关系式，并指出函数的自变量和定义域.</p>
          <p><span class="zt-ls"><b>解</b></span> 体积<i>V</i> 随边长<i>a</i>变化的函数关系式是</p>
          <p class="center"><i>V</i>=<i>a</i><sup>3</sup>（<i>a</i>＞0）.</p>
          <p>其中<i>a</i>是自变量，定义域为{<i>a</i>|<i>a</i>＞0}.</p>
          <p>
            <span>
              <span class="zt-ls"><b>例3</b></span>　如图3-2所示，一个边长是<i>a</i>的正方体，体积是<i>V</i>，写出体积<i>V</i> 随边长<i>a</i>
              变化的函数关系式，并指出函数的自变量和定义域.
            </span>
            <span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer2" >
            <p><span class="zt-ls"><b>解</b></span> 体积<i>V</i> 随边长<i>a</i>变化的函数关系式是</p>
            <p class="center"><i>V</i>=<i>a</i><sup>3</sup>（<i>a</i>＞0）.</p>
            <p>其中<i>a</i>是自变量，定义域为{<i>a</i>|<i>a</i>＞0}.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[78] ? questionData[78][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
@@ -195,42 +232,54 @@
              </mfrac>
            </math>的函数值<i>f</i>（0），因为<i>f</i>（0）无意义，因此，它的定义域是{<i>x</i>｜<i>x</i>≠0}.在实际问题中，函数的定义域通常由问题的实际背景所决定.如例3中的函数<i>V</i>=<i>a</i><sup>3</sup>，由于<i>a</i>是正方体的边长，所以函数的定义域为<i>A</i>={<i>a</i>｜<i>a</i>＞0}.
          </p>
          <p><span
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例4</b></span>　就业是最基本的民生，小凯通过自主创办奶品店实现职业发展.为促销自制酸奶，每瓶酸奶的价格是3.5元，每位顾客最多只能购买50瓶.假设某人购买这种酸奶<i>x</i>瓶，应付款<i>y</i>元.那么<i>y</i>（元）是<i>x</i>（瓶）的函数吗？如果是，请写出函数的定义域、对应关系和值域；如果不是，请说明理由.
            </span>
            <span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>解</b></span>
            <i>x</i>的取值范围是数集<i>A</i>={<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，<i>y</i>的取值范围是数集<i>B</i>={<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.对于集合<i>A</i>中的任一个数<i>x</i>，按照对应关系，在集合<i>B</i>中都有唯一确定的值与之对应，所以应付款<i>y</i>是购买数量<i>x</i>的函数.
          </p>
          <p>
            函数的定义域是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，对应关系是<i>y</i>=3.5<i>x</i>，值域是{<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.
          </p>
          <p>
            例4中函数的定义域为什么是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，而不是{<i>x</i>|<i>x</i>∈<b>R</b>}？这是因为此函数的定义域考虑了函数自变量取值的客观实际背景.
          </p>
          <div v-if="isShowAnswer3" >
            <p><span class="zt-ls"><b>解</b></span>
              <i>x</i>的取值范围是数集<i>A</i>={<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，<i>y</i>的取值范围是数集<i>B</i>={<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.对于集合<i>A</i>中的任一个数<i>x</i>，按照对应关系，在集合<i>B</i>中都有唯一确定的值与之对应，所以应付款<i>y</i>是购买数量<i>x</i>的函数.
            </p>
            <p>
              函数的定义域是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，对应关系是<i>y</i>=3.5<i>x</i>，值域是{<i>y</i>|<i>y</i>=3.5<i>x</i>，<i>x</i>≤50，且<i>x</i>∈<b>N</b>}.
            </p>
            <p>
              例4中函数的定义域为什么是{<i>x</i>|<i>x</i>≤50，<i>x</i>∈<b>N</b>}，而不是{<i>x</i>|<i>x</i>∈<b>R</b>}？这是因为此函数的定义域考虑了函数自变量取值的客观实际背景.
            </p>
          </div>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0083-2.jpg" /></p>
          <p class="img">图3-3</p>
          <p><span
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例5</b></span>　如图3-3所示，在矩形<i>ABCD</i>中，<i>AB</i>的长度是<i>x</i>（m），<i>BC</i>的长度是（12-<i>x</i>）（m），矩形<i>ABCD</i>的面积是<i>y</i>（<i>m</i><sup>2</sup>），则<i>y</i>与<i>x</i>的对应关系是<i>y</i>=<i>x</i>（12-<i>x</i>），求该函数的定义域.
            </span>
            <span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkTwo)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　因为<i>AB</i>的长度为<i>x</i>（m），<i>BC</i>的长度为（12-<i>x</i>）（m），所以必须满足<i>x</i>＞0且12-<i>x</i>＞0才有实际意义.
          </p>
        </div>
      </div>
    </div>
    <!-- 073 -->
    <div class="page-box" page="80">
      <div v-if="showPageList.indexOf(80) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>073</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>解</b></span> 要使函数<i>y</i>=<i>x</i>（12-<i>x</i>）有实际意义，必须满足<math display="0">
          <p v-if="isShowAnswer4" >
            <span class="zt-ls"><b>解</b></span> 要使函数<i>y</i>=<i>x</i>（12-<i>x</i>）有实际意义，必须满足<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
@@ -257,156 +306,211 @@
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>解得0＜<i>x</i>＜12.所以这个函数的定义域是{<i>x</i>|0＜<i>x</i>＜12}.</p>
        </div>
      </div>
    </div>
    <!-- 073 -->
    <div class="page-box" page="80">
      <div v-if="showPageList.indexOf(80) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>073</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例6</b></span>　求下列函数的定义域.</p>
          <p>（1） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mfrac>
                <mn>1</mn>
                <mrow>
                  <mn>4</mn>
          <p class="p-btn" >
            <span>
              （1） <math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>7</mn>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </mfrac>
            </math>；（2）<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <msqrt>
                <mi>x</mi>
                <mo>−</mo>
                <mn>3</mn>
              </msqrt>
            </math>；</p>
          <p>（3） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <msqrt>
                <mn>4</mn>
                <mi>x</mi>
                <mo>+</mo>
                <mn>8</mn>
              </msqrt>
              <mo>+</mo>
              <mfrac>
                <mn>1</mn>
                <mrow>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>3</mn>
                </mrow>
              </mfrac>
            </math>.</p>
          <p><span class="zt-ls"><b>解</b></span>（1） 要使该函数有意义，必须满足</p>
          <p class="center">4<i>x</i>+7≠0，</p>
          <p>解得</p>
          <math display="block">
            <mi>x</mi>
            <mo>≠</mo>
            <mo>−</mo>
            <mfrac>
              <mn>7</mn>
              <mn>4</mn>
            </mfrac>
            <mo>.</mo>
          </math>
          <p>所以函数<i>f</i>（<i>x</i>）的定义域是<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mi>x</mi>
                <mrow>
                  <mo stretchy="false">|</mo>
                </mrow>
                <mi>x</mi>
                <mo>≠</mo>
                <mo>−</mo>
                <mo>=</mo>
                <mfrac>
                  <mn>7</mn>
                  <mn>4</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">}</mo>
              </mrow>
            </math>.</p>
          <p>（2） 要使该函数有意义，必须满足</p>
          <p class="center"><i>x</i>-3≥0，</p>
          <p>解得　<i>x</i>≥3.</p>
          <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥3}.</p>
          <p>（3） 要使该函数有意义，必须满足</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">{</mo>
              <mtable columnspacing="1em" rowspacing="4pt">
                <mtr>
                  <mtd>
                  <mn>1</mn>
                  <mrow>
                    <mn>4</mn>
                    <mi>x</mi>
                    <mo>+</mo>
                    <mn>8</mn>
                    <mo>≥</mo>
                    <mn>0</mn>
                    <mo>，</mo>
                  </mtd>
                  <mtd></mtd>
                </mtr>
                <mtr>
                  <mtd>
                    <mn>7</mn>
                  </mrow>
                </mfrac>
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer5" >
            <p><span class="zt-ls"><b>解</b></span>（1） 要使该函数有意义，必须满足</p>
            <p class="center">4<i>x</i>+7≠0，</p>
            <p>解得</p>
            <math display="block">
              <mi>x</mi>
              <mo>≠</mo>
              <mo>−</mo>
              <mfrac>
                <mn>7</mn>
                <mn>4</mn>
              </mfrac>
              <mo>.</mo>
            </math>
            <p>所以函数<i>f</i>（<i>x</i>）的定义域是<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mi>x</mi>
                  <mrow>
                    <mo stretchy="false">|</mo>
                  </mrow>
                  <mi>x</mi>
                  <mo>≠</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>7</mn>
                    <mn>4</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">}</mo>
                </mrow>
              </math>.</p>
          </div>
          <p class="p-btn">
            <span>
              （2）<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <msqrt>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>3</mn>
                </msqrt>
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer6" >
            <p> <span class="zt-ls"><b>解</b></span>（2） 要使该函数有意义，必须满足</p>
            <p class="center"><i>x</i>-3≥0，</p>
            <p>解得　<i>x</i>≥3.</p>
            <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥3}.</p>
          </div>
          <p class="p-btn" >
            <span>
              （3） <math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <msqrt>
                  <mn>4</mn>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>8</mn>
                </msqrt>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mrow>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>3</mn>
                    <mo>≠</mo>
                    <mn>0</mn>
                    <mo>，</mo>
                  </mtd>
                  <mtd></mtd>
                </mtr>
              </mtable>
              <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
            </mrow>
          </math>
          <p>解得</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">{</mo>
              <mtable columnspacing="1em" rowspacing="4pt">
                <mtr>
                  <mtd>
                    <mi>x</mi>
                    <mo>≥</mo>
                    <mo>−</mo>
                    <mn>2</mn>
                    <mo>，</mo>
                  </mtd>
                  <mtd></mtd>
                </mtr>
                <mtr>
                  <mtd>
                    <mi>x</mi>
                    <mo>≠</mo>
                    <mn>3.</mn>
                  </mtd>
                  <mtd></mtd>
                </mtr>
              </mtable>
              <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
            </mrow>
          </math>
          <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥-2且<i>x</i>≠3}.</p>
                  </mrow>
                </mfrac>
              </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer7" >
            <p> <span class="zt-ls"><b>解</b></span>（3） 要使该函数有意义，必须满足</p>
            <math display="block">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mn>4</mn>
                      <mi>x</mi>
                      <mo>+</mo>
                      <mn>8</mn>
                      <mo>≥</mo>
                      <mn>0</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mi>x</mi>
                      <mo>−</mo>
                      <mn>3</mn>
                      <mo>≠</mo>
                      <mn>0</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>
            <p>解得</p>
            <math display="block">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mi>x</mi>
                      <mo>≥</mo>
                      <mo>−</mo>
                      <mn>2</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mi>x</mi>
                      <mo>≠</mo>
                      <mn>3.</mn>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>
            <p>所以函数<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥-2且<i>x</i>≠3}.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj" >
            <examinations :cardList="questionData[80]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
@@ -435,15 +539,39 @@
          <p>我们知道，上一节“观察思考”中的3个情境都涉及变量之间的函数关系.情境1中，销售收入<i>y</i>（元）与销售量<i>x</i>（kg ）的函数关系是<i>y</i>=6<i>x</i>，0≤<i>x</i>≤2
            000，这种表示函数关系的方法称为解析法；情境2中，用表格表示了发射卫星的颗数<i>y</i>与年份<i>x</i>的函数关系，这种表示函数关系的方法称为列表法；情境3中，用图像表示了气温<i>Q</i>与时间<i>t</i>的函数关系，这种表示函数关系的方法称为图像法.
          </p>
          <p><span class="zt-ls"><b>例1</b></span>　某辆汽车以30 km/<i>h</i> 的速度匀速直线行驶，用解析法表示汽车行驶的路程<i>s</i>（km
            ）与时间<i>t</i>（<i>h</i>）之间的对应关系.</p>
          <p><span class="zt-ls"><b>解</b></span> 这个函数的定义域是{<i>t</i>|<i>t</i>≥0}.</p>
          <p>用解析法可将这个函数表示为<i>s</i>=30<i>t</i>，<i>t</i>≥0.</p>
          <p>用解析法表示函数关系，能够准确、完整地反映两个变量之间的关系.</p>
          <p><span class="zt-ls"><b>例2</b></span>　近年我国快递业务量迅速增长，从2017年至2021年，每年的快递业务量情况如表3-4所示（注：引自国家统计局数据）.</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例1</b></span>　某辆汽车以30 km/<i>h</i> 的速度匀速直线行驶，用解析法表示汽车行驶的路程<i>s</i>（km
              ）与时间<i>t</i>（<i>h</i>）之间的对应关系.
            </span>
            <span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer8" >
            <p><span class="zt-ls"><b>解</b></span> 这个函数的定义域是{<i>t</i>|<i>t</i>≥0}.</p>
            <p>用解析法可将这个函数表示为<i>s</i>=30<i>t</i>，<i>t</i>≥0.</p>
            <p>用解析法表示函数关系，能够准确、完整地反映两个变量之间的关系.</p>
          </div>
          <p>
            <span>
              <span class="zt-ls"><b>例2</b></span>　近年我国快递业务量迅速增长，从2017年至2021年，每年的快递业务量情况如表3-4所示（注：引自国家统计局数据）.
            </span>
            <span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">表3-4</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0087-2.jpg" /></p>
          <p>表3-4清晰地反映了年份与当年快递业务量（亿件）之间的对应关系.在实际生活中，用列表法表示变量之间对应关系的例子还有很多.例如，记录某人每天的消费情况、单位职工的每月薪资收入、银行使用的存款“利息表”等.</p>
          <p v-if="isShowAnswer9" >表3-4清晰地反映了年份与当年快递业务量（亿件）之间的对应关系.在实际生活中，用列表法表示变量之间对应关系的例子还有很多.例如，记录某人每天的消费情况、单位职工的每月薪资收入、银行使用的存款“利息表”等.</p>
        </div>
      </div>
    </div>
@@ -465,36 +593,88 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>观察上一节“观察思考”中的情境3，我们发现用图像法表示函数关系时能直观形象地表示出函数的局部变化规律，进而可以预测它的整体变化趋势.但是我们并不能作出所有函数的图像.</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-1.jpg" /></p>
          <p class="img">图3-4</p>
          <p><span
              class="zt-ls"><b>例3</b></span>　使用环保毛巾替代一次性纸巾，是倡导低碳环保生活的一种方式.某便民超市促销某种小毛巾，每条售价4元，每人限购5条.若顾客购买<i>x</i>条小毛巾需要付款<i>y</i>元，试用图像法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.
          </p>
          <p><span class="zt-ls"><b>解</b></span> 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{1，2，3，4，5}，用图像法可将这个函数表示为图3-4.</p>
          <div v-if="isShowAnswer9" >
            <p>观察上一节“观察思考”中的情境3，我们发现用图像法表示函数关系时能直观形象地表示出函数的局部变化规律，进而可以预测它的整体变化趋势.但是我们并不能作出所有函数的图像.</p>
          </div>
          <p>
            函数的图像既可以是离散的点，也可以是线段、直线、折线、连续的曲线等.在初中，我们用列表、描点、连线的方法画出了正比例函数、反比例函数、一次函数和二次函数的图像.图像法也被大量用于各类数据统计中.例如，GDP（国内生产总值）每年的增长情况、居民消费价格每季度的增长情况、全国人口数量每年的变化情况等.
            <span>
              <span
                class="zt-ls"><b>例3</b></span>　使用环保毛巾替代一次性纸巾，是倡导低碳环保生活的一种方式.某便民超市促销某种小毛巾，每条售价4元，每人限购5条.若顾客购买<i>x</i>条小毛巾需要付款<i>y</i>元，试用图像法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.
            </span>
            <span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>例4</b></span>　一艘军舰与某海港相距135 n mile（1 n mile ≈1.852 km ），如果军舰以45 n mile/h 的速度向海港前行，则3
            h后可到达海港.假设这艘军舰出发t（h）后，与海港的距离是s（n mile）.</p>
          <p>（1） 用解析法表示函数<i>s</i>=<i>f</i>（<i>t</i>）；</p>
          <p>（2） 用图像法表示函数<i>s</i>=<i>f</i>（<i>t</i>）.</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　计算该军舰从出发地驶入海港所需要的时间，就可得到函数<i>s</i>=<i>f</i>（<i>t</i>）的定义域.用解析法表示函数后，再画出函数的图像.
          <div v-if="isShowAnswer10" > 
            <p><span class="zt-ls"><b>解</b></span> 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{1，2，3，4，5}，用图像法可将这个函数表示为图3-4.</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-1.jpg" /></p>
            <p class="img">图3-4</p>
            <p>
              函数的图像既可以是离散的点，也可以是线段、直线、折线、连续的曲线等.在初中，我们用列表、描点、连线的方法画出了正比例函数、反比例函数、一次函数和二次函数的图像.图像法也被大量用于各类数据统计中.例如，GDP（国内生产总值）每年的增长情况、居民消费价格每季度的增长情况、全国人口数量每年的变化情况等.
            </p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <p>
            <span>
              <span class="zt-ls"><b>例4</b></span>　一艘军舰与某海港相距135 n mile（1 n mile ≈1.852 km ），如果军舰以45 n mile/h 的速度向海港前行，则3
              h后可到达海港.假设这艘军舰出发t（h）后，与海港的距离是s（n mile）.
            </span>
            <span class="btn-box" @click="openDialog(thinkThree)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>解</b></span>（1） 因为该军舰从出发地驶入海港需要用时<math display="0">
              <mfrac>
                <mn>135</mn>
                <mn>45</mn>
              </mfrac>
              <mo>=</mo>
              <mn>3</mn>
              <mo>（</mo>
              <mi>h</mi>
              <mo>）</mo>
            </math>，所以函数的定义域为{<i>t</i>|0≤<i>t</i>≤3}.</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-3.jpg" /></p>
          <p class="img">图3-5</p>
          <p class="p-btn" >
            <span>
              （1） 用解析法表示函数<i>s</i>=<i>f</i>（<i>t</i>）；
            </span>
            <span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer11" > 
            <p><span class="zt-ls"><b>解</b></span>（1） 因为该军舰从出发地驶入海港需要用时<math display="0">
                <mfrac>
                  <mn>135</mn>
                  <mn>45</mn>
                </mfrac>
                <mo>=</mo>
                <mn>3</mn>
                <mo>（</mo>
                <mi>h</mi>
                <mo>）</mo>
              </math>，所以函数的定义域为{<i>t</i>|0≤<i>t</i>≤3}.
            </p>
            <p>又因为该军舰出发<i>t</i>（<i>h</i>）后，行驶的路程为45<i>t n mile</i> ，这时该军舰与海港的距离为（135-45<i>t</i>） <i>n mile</i> .</p>
            <p>所以，用解析法可将函数<i>s</i>=<i>f</i>（<i>t</i>）表示为</p>
            <p class="center"><i>s</i>=-45<i>t</i>+135，0≤<i>t</i>≤3.</p>
          </div>
          <p class="p-btn" >
            <span>（2） 用图像法表示函数<i>s</i>=<i>f</i>（<i>t</i>）.</span>
            <span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer12" >
            <p> <span class="zt-ls"><b>解</b></span>（2） 函数<i>s</i>=<i>f</i>（<i>t</i>）是一次函数，用图像法可将函数表示为图3-5.</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0088-3.jpg" /></p>
            <p class="img">图3-5</p>
          </div>
        </div>
      </div>
    </div>
@@ -507,10 +687,6 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>又因为该军舰出发<i>t</i>（<i>h</i>）后，行驶的路程为45<i>t n mile</i> ，这时该军舰与海港的距离为（135-45<i>t</i>） <i>n mile</i> .</p>
          <p>所以，用解析法可将函数<i>s</i>=<i>f</i>（<i>t</i>）表示为</p>
          <p class="center"><i>s</i>=-45<i>t</i>+135，0≤<i>t</i>≤3.</p>
          <p>（2） 函数<i>s</i>=<i>f</i>（<i>t</i>）是一次函数，用图像法可将函数表示为图3-5.</p>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
@@ -712,7 +888,22 @@
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math></p>
          <p>（1） 求<i>f</i>（-5），<i>f</i>（4）的值；</p>
          <p class="p-btn" >
            <span>
              （1） 求<i>f</i>（-5），<i>f</i>（4）的值；
            </span>
            <span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer13" >
            <p><span class="zt-ls"><b>解</b></span>（1） 因为-5＜0，所以<i>f</i>（-5）=-5+2=-3.</p>
            <p>因为4＞0，所以 <i>f</i>（4）=4<sup>2</sup>-3=13.</p>
          </div>
        </div>
      </div>
    </div>
@@ -725,7 +916,20 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p>（2） 求<i>f</i>（<i>f</i>（-1））的值.</p>
          <p class="p-btn" >
            <span>（2） 求<i>f</i>（<i>f</i>（-1））的值.</span>
            <span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer14">
            <p>  <span class="zt-ls"><b>解</b></span>（2） 因为-1＜0，所以<i>f</i>（-1）=-1+2=1.</p>
            <p>又因为1＞0，所以<i>f</i>（<i>f</i>（-1））=<i>f</i>（1）=1<sup>2</sup>-3=-2.</p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
@@ -734,89 +938,130 @@
              分段函数是一个函数，不能把它看成几个函数，只是在同一个函数的定义域内，不同的取值范围内对应不同的函数关系.它的定义域是各个解析式的自变量取值集合的并集，值域也是各个解析式的函数值集合的并集.它的图像也比较特殊，有时图像是不连续的.
            </p>
          </div>
          <p><span class="zt-ls"><b>解</b></span>（1） 因为-5＜0，所以<i>f</i>（-5）=-5+2=-3.</p>
          <p>因为4＞0，所以 <i>f</i>（4）=4<sup>2</sup>-3=13.</p>
          <p>（2） 因为-1＜0，所以<i>f</i>（-1）=-1+2=1.</p>
          <p>又因为1＞0，所以<i>f</i>（<i>f</i>（-1））=<i>f</i>（1）=1<sup>2</sup>-3=-2.</p>
          <p><span
          <p>
            <span
              class="zt-ls"><b>例2</b></span>　我国是用电量最大的国家，国家发出节能减排的号召，鼓励居民节约用电，2019年国家对居民每月用电量进行划分，电价施行“分档递增”.某城市居民每月用电计费价格如表3-7所示.假设这个城市的某居民某月用电量是<i>x</i>（kW·h），需支付电费<i>y</i>（元）.
            <span class="btn-box" @click="openDialog(thinkFour)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="img">表3-7 某城市居民每月用电计费价格表</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0091-1.jpg" /></p>
          <p>（1） 用解析法表示<i>y</i>与<i>x</i>的函数关系，并画出函数的图像.</p>
          <p>（2） 如果李某家10月的用电量是180 kW·h ，那么他家应该支付电费多少？</p>
          <p>（3） 如果周某家12月支付电费294.26元，那么他家这个月的用电量是多少？</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　首先需明确这个函数的定义域.由于居民用电量不同，其收费标准也不同，所以这是分段函数.其次要厘清自变量<i>x</i>在不同的取值范围内与因变量<i>y</i>之间的对应关系，并列出相应的解析式来解决相关问题.
          <p class="p-btn" >
            <span>（1） 用解析法表示<i>y</i>与<i>x</i>的函数关系，并画出函数的图像.</span>
            <span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>解</b></span>（1） 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥0}.</p>
          <p>当0≤<i>x</i>≤200时，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=0.52<i>x</i>；</p>
          <p>当200＜<i>x</i>≤400时，<i>y</i>与<i>x</i>的对应关系是</p>
          <p class="center"><i>y</i>=0.52×200+0.57（<i>x</i>-200）=0.57<i>x</i>-10；</p>
          <p>当<i>x</i>＞400时，<i>y</i>与<i>x</i>的对应关系是</p>
          <p><i>y</i>=0.52×200+0.57×200+0.82（<i>x</i>-400）=0.82<i>x</i>-110.</p>
          <p>用解析法表示<i>y</i>与<i>x</i>的函数关系如下.</p>
          <math display="block">
            <mi>y</mi>
            <mo>=</mo>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">{</mo>
              <mtable columnspacing="1em" rowspacing="4pt">
                <mtr>
                  <mtd>
                    <mn>0.52</mn>
                    <mi>x</mi>
                    <mo>，</mo>
                    <mn>0</mn>
                    <mo>≤</mo>
                    <mi>x</mi>
                    <mo>≤</mo>
                    <mn>200</mn>
                    <mo>，</mo>
                  </mtd>
                  <mtd></mtd>
                  <mtd></mtd>
                  <mtd></mtd>
                </mtr>
                <mtr>
                  <mtd>
                    <mn>0.57</mn>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>10</mn>
                    <mo>，</mo>
                    <mn>200</mn>
                    <mo>＜</mo>
                    <mi>x</mi>
                    <mo>≤</mo>
                    <mn>400</mn>
                    <mo>，</mo>
                  </mtd>
                  <mtd></mtd>
                  <mtd></mtd>
                  <mtd></mtd>
                </mtr>
                <mtr>
                  <mtd>
                    <mn>0.82</mn>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>110</mn>
                    <mo>，</mo>
                    <mi>x</mi>
                    <mo>＞</mo>
                    <mn>400.</mn>
                  </mtd>
                  <mtd></mtd>
                  <mtd></mtd>
                  <mtd></mtd>
                </mtr>
              </mtable>
              <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
            </mrow>
          </math>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0092-1.jpg" /></p>
          <p class="img">图3-7</p>
          <div v-if="isShowAnswer15" >
            <p><span class="zt-ls"><b>解</b></span>（1） 函数<i>y</i>=<i>f</i>（<i>x</i>）的定义域是{<i>x</i>|<i>x</i>≥0}.</p>
            <p>当0≤<i>x</i>≤200时，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=0.52<i>x</i>；</p>
            <p>当200＜<i>x</i>≤400时，<i>y</i>与<i>x</i>的对应关系是</p>
            <p class="center"><i>y</i>=0.52×200+0.57（<i>x</i>-200）=0.57<i>x</i>-10；</p>
            <p>当<i>x</i>＞400时，<i>y</i>与<i>x</i>的对应关系是</p>
            <p><i>y</i>=0.52×200+0.57×200+0.82（<i>x</i>-400）=0.82<i>x</i>-110.</p>
            <p>用解析法表示<i>y</i>与<i>x</i>的函数关系如下.</p>
            <math display="block">
              <mi>y</mi>
              <mo>=</mo>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mn>0.52</mn>
                      <mi>x</mi>
                      <mo>，</mo>
                      <mn>0</mn>
                      <mo>≤</mo>
                      <mi>x</mi>
                      <mo>≤</mo>
                      <mn>200</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                    <mtd></mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mn>0.57</mn>
                      <mi>x</mi>
                      <mo>−</mo>
                      <mn>10</mn>
                      <mo>，</mo>
                      <mn>200</mn>
                      <mo>＜</mo>
                      <mi>x</mi>
                      <mo>≤</mo>
                      <mn>400</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                    <mtd></mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mn>0.82</mn>
                      <mi>x</mi>
                      <mo>−</mo>
                      <mn>110</mn>
                      <mo>，</mo>
                      <mi>x</mi>
                      <mo>＞</mo>
                      <mn>400.</mn>
                    </mtd>
                    <mtd></mtd>
                    <mtd></mtd>
                    <mtd></mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0092-1.jpg" /></p>
            <p class="img">图3-7</p>
            <p>这个函数的图像如图3-7所示.</p>
          </div>
          <p class="p-btn" >
            <span>（2） 如果李某家10月的用电量是180 kW·h ，那么他家应该支付电费多少？</span>
            <span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer16" >
            <p> <span class="zt-ls"><b>解</b></span>（2） 因为<i>x</i>=180＜200，<i>y</i>=0.52×180=93.60（元）.</p>
            <p>所以，李某家10月应该支付电费93.60元.</p>
          </div>
          <p class="p-btn" >
            <span>（3） 如果周某家12月支付电费294.26元，那么他家这个月的用电量是多少？</span>
            <span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer17" >
            <p> <span class="zt-ls"><b>解</b></span>（3） 周某家电费是294.26元，由图3-7可估得<i>x</i>＞400，因此</p>
            <p class="center">0.82<i>x</i>-110=294.26，</p>
            <p>解得<i>x</i>=493.</p>
            <p>所以，周某家12月的用电量为493 kW·h .</p>
          </div>
        </div>
      </div>
    </div>
@@ -832,13 +1077,7 @@
          </li>
        </ul>
        <div class="padding-116">
          <p>这个函数的图像如图3-7所示.</p>
          <p>（2） 因为<i>x</i>=180＜200，<i>y</i>=0.52×180=93.60（元）.</p>
          <p>所以，李某家10月应该支付电费93.60元.</p>
          <p>（3） 周某家电费是294.26元，由图3-7可估得<i>x</i>＞400，因此</p>
          <p class="center">0.82<i>x</i>-110=294.26，</p>
          <p>解得<i>x</i>=493.</p>
          <p>所以，周某家12月的用电量为493 kW·h .</p>

          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
@@ -947,12 +1186,32 @@
            例如，图3-8中函数<i>y</i>=<i>x</i>是<b>R</b>上的增函数，区间（-∞，+∞）是函数<i>y</i>=<i>x</i>的增区间；函数<i>y</i>=-<i>x</i>是<b>R</b>上的减函数，区间（-∞，+∞）是函数<i>y</i>=-<i>x</i>的减区间；函数<i>y</i>=<i>x</i><sup>2</sup>在区间（-∞，0）上是减函数，在区间（0，+∞）上是增函数，区间（-∞，0）和（0，+∞）分别是函数<i>y</i>=<i>x</i><sup>2</sup>的减区间、增区间.
          </p>
          <p><span class="zt-ls"><b>例1</b></span>　图3-11是函数<i>y</i>=<i>f</i>（<i>x</i>），<i>x</i>∈［-1，8］的图像，根据图像回答下列问题.</p>
          <p>（1） 当<i>x</i>取何值时，函数值最大，最大值是多少？当<i>x</i>取何值时，函数值最小，最小值是多少？</p>
          <p>（2） 说明该函数的单调区间及在每一个区间上的单调性.</p>
          <p  class="p-btn" >
            <span>（1） 当<i>x</i>取何值时，函数值最大，最大值是多少？当<i>x</i>取何值时，函数值最小，最小值是多少？</span>
            <span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer18" ><span class="zt-ls"><b>解</b></span>（1） 由图可知，当<i>x</i>=2时，函数值最大，最大值是3；当<i>x</i>=6时，函数值最小，最小值是-3.</p>
          <p class="p-btn" >
            <span>（2） 说明该函数的单调区间及在每一个区间上的单调性.</span>
            <span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0097-3.jpg" /></p>
          <p class="img">图3-11</p>
          <p><span class="zt-ls"><b>解</b></span>（1） 由图可知，当<i>x</i>=2时，函数值最大，最大值是3；当<i>x</i>=6时，函数值最小，最小值是-3.</p>
          <p>（2）
          <p v-if="isShowAnswer19" >
            <span class="zt-ls"><b>解</b></span>
            （2）
            函数<i>y</i>=<i>f</i>（<i>x</i>）的单调区间有［-1，2］，［2，6］，［6，8］.函数<i>y</i>=<i>f</i>（<i>x</i>）在区间［-1，2］和［6，8］上都是增函数，在区间［2，6］上是减函数.
          </p>
        </div>
@@ -974,24 +1233,21 @@
          <p class="img">图3-12</p>
          <p><span class="zt-ls"><b>例2</b></span>　二次函数<i>f</i>（<i>x</i>）=-<i>x</i><sup>2</sup>+2<i>x</i>+3的图像如图3-12所示.
          </p>
          <p>（1） 求函数<i>f</i>（<i>x</i>）的对称轴方程、顶点坐标；</p>
          <p>（2） 找出函数<i>f</i>（<i>x</i>）的单调区间；</p>
          <p>（3） 当<i>x</i>∈［2，5］时，求函数<i>f</i>（<i>x</i>）的最大值和最小值.</p>
          <p><span class="zt-ls"><b>解</b></span>（1） 二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>的对称轴方程是<math
              display="0">
              <mi>x</mi>
              <mo>=</mo>
              <mfrac>
                <mi>b</mi>
                <mrow>
                  <mn>2</mn>
                  <mi>a</mi>
                </mrow>
              </mfrac>
            </math>，顶点坐标是<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
          <p class="p-btn" >
            <span>（1） 求函数<i>f</i>（<i>x</i>）的对称轴方程、顶点坐标；</span>
            <span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer20" >
            <p><span class="zt-ls"><b>解</b></span>（1） 二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>的对称轴方程是<math
                display="0">
                <mi>x</mi>
                <mo>=</mo>
                <mfrac>
                  <mi>b</mi>
                  <mrow>
@@ -999,32 +1255,9 @@
                    <mi>a</mi>
                  </mrow>
                </mfrac>
                <mo>，</mo>
                <mfrac>
                  <mrow>
                    <mn>4</mn>
                    <mi>a</mi>
                    <mi>c</mi>
                    <mo>−</mo>
                    <msup>
                      <mi>b</mi>
                      <mrow>
                        <mn>2</mn>
                      </mrow>
                    </msup>
                  </mrow>
                  <mrow>
                    <mn>4</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，则</p>
          <math display="block">
            <mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
              <mtr>
                <mtd>
              </math>，顶点坐标是<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mi>b</mi>
@@ -1033,25 +1266,7 @@
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo>=</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>2</mn>
                    <mrow>
                      <mn>2</mn>
                      <mo>×</mo>
                      <mo stretchy="false">(</mo>
                      <mo>−</mo>
                      <mn>1</mn>
                      <mo stretchy="false">)</mo>
                    </mrow>
                  </mfrac>
                  <mo>=</mo>
                  <mn>1，</mn>
                </mtd>
              </mtr>
              <mtr>
                <mtd>
                  <mo>，</mo>
                  <mfrac>
                    <mrow>
                      <mn>4</mn>
@@ -1070,69 +1285,158 @@
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo>=</mo>
                  <mfrac>
                    <mrow>
                      <mn>4</mn>
                      <mo>×</mo>
                      <mo stretchy="false">(</mo>
                      <mo>−</mo>
                      <mn>1</mn>
                      <mo stretchy="false">)</mo>
                      <mo>×</mo>
                      <mn>3</mn>
                      <mo>−</mo>
                      <msup>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，则</p>
            <math display="block">
              <mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
                <mtr>
                  <mtd>
                    <mo>−</mo>
                    <mfrac>
                      <mi>b</mi>
                      <mrow>
                        <mn>2</mn>
                        <mrow>
                        <mi>a</mi>
                      </mrow>
                    </mfrac>
                    <mo>=</mo>
                    <mo>−</mo>
                    <mfrac>
                      <mn>2</mn>
                      <mrow>
                        <mn>2</mn>
                        <mo>×</mo>
                        <mo stretchy="false">(</mo>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo stretchy="false">)</mo>
                      </mrow>
                    </mfrac>
                    <mo>=</mo>
                    <mn>1，</mn>
                  </mtd>
                </mtr>
                <mtr>
                  <mtd>
                    <mfrac>
                      <mrow>
                        <mn>4</mn>
                        <mi>a</mi>
                        <mi>c</mi>
                        <mo>−</mo>
                        <msup>
                          <mi>b</mi>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                        <mi>a</mi>
                      </mrow>
                    </mfrac>
                    <mo>=</mo>
                    <mfrac>
                      <mrow>
                        <mn>4</mn>
                        <mo>×</mo>
                        <mo stretchy="false">(</mo>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo stretchy="false">)</mo>
                        <mo>×</mo>
                        <mn>3</mn>
                        <mo>−</mo>
                        <msup>
                          <mn>2</mn>
                        </mrow>
                      </msup>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                      <mo>×</mo>
                      <mo stretchy="false">(</mo>
                      <mo>−</mo>
                      <mn>1</mn>
                      <mo stretchy="false">)</mo>
                    </mrow>
                  </mfrac>
                  <mo>=</mo>
                  <mn>4</mn>
                  <mo>.</mo>
                </mtd>
              </mtr>
            </mtable>
          </math>
          <p>因此，函数<i>f</i>（<i>x</i>）的对称轴方程是<i>x</i>=1，顶点坐标是（1，4）.</p>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                      </mrow>
                      <mrow>
                        <mn>4</mn>
                        <mo>×</mo>
                        <mo stretchy="false">(</mo>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo stretchy="false">)</mo>
                      </mrow>
                    </mfrac>
                    <mo>=</mo>
                    <mn>4</mn>
                    <mo>.</mo>
                  </mtd>
                </mtr>
              </mtable>
            </math>
            <p>因此，函数<i>f</i>（<i>x</i>）的对称轴方程是<i>x</i>=1，顶点坐标是（1，4）.</p>
          </div>
          <p class="p-btn" >
            <span>（2） 找出函数<i>f</i>（<i>x</i>）的单调区间；</span>
            <span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer21" > <span class="zt-ls"><b>解</b></span>（2） 由图像可知，函数<i>f</i>（<i>x</i>）的增区间是（-∞，1］，减区间是［1，+∞）.</p>
          <p class="p-btn" >
            <span>（3） 当<i>x</i>∈［2，5］时，求函数<i>f</i>（<i>x</i>）的最大值和最小值.</span>
            <span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer22" >
            <p> <span class="zt-ls"><b>解</b></span>（3） 因为［2，5］⫋［1，+∞），且函数在区间［1，+∞）上是减函数，所以当<i>x</i>∈［2，5］时，</p>
            <p>函数<i>f</i>（<i>x</i>）的最大值是<i>f</i>（2）=-2<sup>2</sup>+2×2+3=3，</p>
            <p>函数<i>f</i>（<i>x</i>）的最小值是<i>f</i>（5）=-5<sup>2</sup>+2×5+3=-12.</p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" /></p>
            </div>
            <p class="block">函数的单调性是对定义域内某个区间而言的.一个函数在其定义域上不一定具有单调性，但是在定义域内的子区间上可能具有单调性，这就是函数单调性的局部性质.</p>
          </div>
          <p>（2） 由图像可知，函数<i>f</i>（<i>x</i>）的增区间是（-∞，1］，减区间是［1，+∞）.</p>
          <p>（3） 因为［2，5］⫋［1，+∞），且函数在区间［1，+∞）上是减函数，所以当<i>x</i>∈［2，5］时，</p>
          <p>函数<i>f</i>（<i>x</i>）的最大值是<i>f</i>（2）=-2<sup>2</sup>+2×2+3=3，</p>
          <p>函数<i>f</i>（<i>x</i>）的最小值是<i>f</i>（5）=-5<sup>2</sup>+2×5+3=-12.</p>
          <p><span class="zt-ls"><b>例3</b></span>　判断函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上的单调性.</p>
          <p><span class="zt-ls"><b>解</b></span>
            任取<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>∈（-∞，+∞），且<i>x</i><sub>1</sub>＜<i>x</i><sub>2</sub>，那么</p>
          <p class="center">
            <i>f</i>（<i>x</i><sub>1</sub>）=<i>x</i><sub>1</sub>+1，<i>f</i>（<i>x</i><sub>2</sub>）=<i>x</i><sub>2</sub>+1，
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例3</b></span>　判断函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上的单调性.
            </span>
            <span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>则</p>
          <p class="center">
            <i>f</i>（<i>x</i><sub>1</sub>）-<i>f</i>（<i>x</i><sub>2</sub>）=<i>x</i><sub>1</sub>+1-<i>x</i><sub>2</sub>-1=<i>x</i><sub>1</sub>-<i>x</i><sub>2</sub>＜0，
          </p>
          <p>
            所以<i>f</i>（<i>x</i><sub>1</sub>）＜<i>f</i>（<i>x</i><sub>2</sub>），函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上是增函数.
          </p>
          <p>当<i>k</i>＞0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是增函数，如图3-13（1）
            所示；当<i>k</i>＜0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是减函数，如图3-13（2） 所示.</p>
          <p class="center"><img class="img-b" alt="" src="../../assets/images/0098-5.jpg" /></p>
          <p class="img">图3-13</p>
          <div v-if="isShowAnswer23" >
            <p><span class="zt-ls"><b>解</b></span>
              任取<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>∈（-∞，+∞），且<i>x</i><sub>1</sub>＜<i>x</i><sub>2</sub>，那么</p>
            <p class="center">
              <i>f</i>（<i>x</i><sub>1</sub>）=<i>x</i><sub>1</sub>+1，<i>f</i>（<i>x</i><sub>2</sub>）=<i>x</i><sub>2</sub>+1，
            </p>
            <p>则</p>
            <p class="center">
              <i>f</i>（<i>x</i><sub>1</sub>）-<i>f</i>（<i>x</i><sub>2</sub>）=<i>x</i><sub>1</sub>+1-<i>x</i><sub>2</sub>-1=<i>x</i><sub>1</sub>-<i>x</i><sub>2</sub>＜0，
            </p>
            <p>
              所以<i>f</i>（<i>x</i><sub>1</sub>）＜<i>f</i>（<i>x</i><sub>2</sub>），函数<i>f</i>（<i>x</i>）=<i>x</i>+1在（-∞，+∞）上是增函数.
            </p>
            <p>当<i>k</i>＞0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是增函数，如图3-13（1）
              所示；当<i>k</i>＜0时，函数<i>f</i>（<i>x</i>）=<i>kx</i>+<i>b</i>在区间（-∞，+∞）上是减函数，如图3-13（2） 所示.</p>
            <p class="center"><img class="img-b" alt="" src="../../assets/images/0098-5.jpg" /></p>
            <p class="img">图3-13</p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
        </div>
      </div>
    </div>
@@ -1310,17 +1614,20 @@
            <img class="img-c" alt="" src="../../assets/images/0102-1.jpg" style="width: 40%" />
          </p>
          <p class="img">图3-17</p>
          <p v-if="isShowExampleTwo">
            <span class="zt-ls"><b>解</b></span>
            函数<i>f</i>（<i>x</i>）=|<i>x</i>|+1的定义域是（-∞，+∞），因为它是偶函数，所以根据其图像关于<i>y</i>轴对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0］上的图像.
          </p>
          <p>
            如图3-18所示，在<i>y</i>轴右边的图像上取两点<i>A</i>和<i>B</i>，分别画出它们关于<i>y</i>轴对称的点<i>A</i>′和<i>B</i>′，然后连线<i>A</i>′<i>B</i>′，就得到这个函数的图像在<i>y</i>轴左边的部分.
          </p>
          <p class="center openImgBox">
            <img class="img-c" alt="" src="../../assets/images/0102-2.jpg" style="width: 40%" />
          </p>
          <p class="img">图3-18</p>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div v-if="isShowExampleTwo">
            <p>
              <span class="zt-ls"><b>解</b></span>
              函数<i>f</i>（<i>x</i>）=|<i>x</i>|+1的定义域是（-∞，+∞），因为它是偶函数，所以根据其图像关于<i>y</i>轴对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0］上的图像.
            </p>
            <p>
              如图3-18所示，在<i>y</i>轴右边的图像上取两点<i>A</i>和<i>B</i>，分别画出它们关于<i>y</i>轴对称的点<i>A</i>′和<i>B</i>′，然后连线<i>A</i>′<i>B</i>′，就得到这个函数的图像在<i>y</i>轴左边的部分.
            </p>
            <p class="center openImgBox">
              <img class="img-c" alt="" src="../../assets/images/0102-2.jpg" style="width: 40%" />
            </p>
            <p class="img">图3-18</p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left">
@@ -1344,24 +1651,11 @@
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                      transform="translate(-3316.14 15289.201)" />
                    <path class="a"
                      d="M316.806,239.727a.6.6,0,1,0,.6-.6A.6.6,0,0,0,316.806,239.727Zm-5.421-4.207a.6.6,0,1,0,.6.6A.587.587,0,0,0,311.385,235.52Zm2.4,8.438a.607.607,0,1,0-.6-.613A.621.621,0,0,0,313.789,243.958Z"
                      transform="translate(-196.896 -148.921)" />
                    <path class="a" d="M763.392,793.79l3.262-3.262h-3.262Z" transform="translate(-638.661 -690.634)" />
                  </g>
                </svg>
              </span>
              <span class="btn-box" @click="openMathDiaolog">
@@ -1561,10 +1855,21 @@
          <p>我们也可以由函数图像是否关于原点中心对称来判断函数是不是奇函数.</p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0105-1.jpg" /></p>
          <p class="img">图3-20</p>
          <p><span class="zt-ls"><b>例4</b></span>　根据图3-21中函数的图像，判断哪些函数是奇函数.</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例4</b></span>　根据图3-21中函数的图像，判断哪些函数是奇函数.
            </span>
            <span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-b" alt="" src="../../assets/images/0105-2.jpg" /></p>
          <p class="img">图3-21</p>
          <p><span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数图像关于原点中心对称；图3-21（4）
          <p v-if="isShowAnswer24" ><span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数图像关于原点中心对称；图3-21（4）
            的函数图像不是关于原点中心对称的.根据奇函数的图像具有关于原点中心对称的特点，图3-21（1） 、图3-21（2） 和图3-21（3） 的函数是奇函数，图3-21（4） 的函数不是奇函数.</p>
        </div>
      </div>
@@ -1581,112 +1886,111 @@
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例5</b></span>　已知函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>图像在<i>y</i>轴右边的部分如图3-22所示.试画出这个函数图像在<i>y</i>轴左边的部分.</p>
          <p><span class="zt-ls"><b>解</b></span> 函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>的定义域是（-∞，0）∪（0+∞），因为它是奇函数，所以根据其图像关于原点中心对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0）上的图像.</p>
          <p>
            如图3-23所示，在<i>y</i>轴右边的图像上取三个不同点<i>A</i>，<i>B</i>和<i>C</i>，并画出它们分别关于原点对称的点<i>A</i>′，<i>B</i>′和<i>C</i>′，然后按相同方式用光滑的曲线连线，就得到这个函数的图像在<i>y</i>轴左边的部分.
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例5</b></span>　已知函数<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
              </math>图像在<i>y</i>轴右边的部分如图3-22所示.试画出这个函数图像在<i>y</i>轴左边的部分.
            </span>
            <span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-3.jpg" /></p>
          <p class="img">图3-22</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-4.jpg" /></p>
          <p class="img">图3-23</p>
          <p>与偶函数的判定方法类似，除了借助函数的图像来判断函数是不是奇函数，也可用定义判断函数是不是奇函数.</p>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div v-if="isShowAnswer25" >
            <p><span class="zt-ls"><b>解</b></span> 函数<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
              </math>的定义域是（-∞，0）∪（0+∞），因为它是奇函数，所以根据其图像关于原点中心对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0）上的图像.</p>
            <p>
              如图3-23所示，在<i>y</i>轴右边的图像上取三个不同点<i>A</i>，<i>B</i>和<i>C</i>，并画出它们分别关于原点对称的点<i>A</i>′，<i>B</i>′和<i>C</i>′，然后按相同方式用光滑的曲线连线，就得到这个函数的图像在<i>y</i>轴左边的部分.
            </p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0106-4.jpg" /></p>
            <p class="img">图3-23</p>
            <p>与偶函数的判定方法类似，除了借助函数的图像来判断函数是不是奇函数，也可用定义判断函数是不是奇函数.</p>
          </div>
          <p><span class="zt-ls"><b>例6</b></span>　判断下列函数是不是奇函数.</p>
          <p>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>；（2） <math display="0">
          <p class="p-btn" >
            <span>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>；</span>
            <span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer26" >
            <p><span class="zt-ls"><b>解</b></span>（1）
              函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
            </p>
            <p class="center">
              <i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>3</sup>+（-<i>x</i>）=-<i>x</i><sup>3</sup>-<i>x</i>=-（<i>x</i><sup>3</sup>+<i>x</i>）=-<i>f</i>（<i>x</i>）.
            </p>
            <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>是奇函数.</p>
          </div>
          <p class="p-btn" >
            <span>
              （2） <math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mi>x</mi>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer27 = !isShowAnswer27">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer27" >
            <p>
              <span class="zt-ls"><b>解</b></span>（2）
              要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，且
            </p>
            <math display="block">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>；（3） <i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|.</p>
          <p><span class="zt-ls"><b>解</b></span>（1）
            函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
          </p>
          <p class="center">
            <i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>3</sup>+（-<i>x</i>）=-<i>x</i><sup>3</sup>-<i>x</i>=-（<i>x</i><sup>3</sup>+<i>x</i>）=-<i>f</i>（<i>x</i>）.
          </p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>3</sup>+<i>x</i>是奇函数.</p>
          <p>（2）
            要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，且
          </p>
          <math display="block">
            <mi>f</mi>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mo>−</mo>
              <mi>x</mi>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>=</mo>
            <mo>−</mo>
            <mi>x</mi>
            <mo>+</mo>
            <mfrac>
              <mn>1</mn>
              <mrow>
                <mo>−</mo>
                <mi>x</mi>
              </mrow>
            </mfrac>
            <mo>=</mo>
            <mo>−</mo>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>=</mo>
            <mo>−</mo>
            <mi>f</mi>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>.</mo>
          </math>
          <p>所以，函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
@@ -1695,10 +1999,68 @@
              <mo>+</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
                <mrow>
                  <mo>−</mo>
                  <mi>x</mi>
                </mrow>
              </mfrac>
            </math>是奇函数.</p>
          <p>（3） 函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，但是</p>
              <mo>=</mo>
              <mo>−</mo>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mo>−</mo>
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>.</mo>
            </math>
            <p>所以，函数<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mo>−</mo>
                <mi>x</mi>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
              </math>是奇函数.
            </p>
          </div>
          <p class="p-btn" >
            <span>（3） <i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|.</span>
            <span class="btn-box" @click="isShowAnswer28 = !isShowAnswer28">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer28"  >
            <p > <span class="zt-ls"><b>解</b></span>（3） 函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，但是</p>
            <p class="center">
              <i>f</i>（-<i>x</i>）=（-<i>x</i>）+|-<i>x</i>|=-<i>x</i>+|<i>x</i>|=-（<i>x</i>-|<i>x</i>|）≠-<i>f</i>（<i>x</i>）.
            </p>
            <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|不是奇函数.</p>
          </div>
        </div>
      </div>
    </div>
@@ -1711,10 +2073,6 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="center">
            <i>f</i>（-<i>x</i>）=（-<i>x</i>）+|-<i>x</i>|=-<i>x</i>+|<i>x</i>|=-（<i>x</i>-|<i>x</i>|）≠-<i>f</i>（<i>x</i>）.
          </p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i>+|<i>x</i>|不是奇函数.</p>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
@@ -1726,133 +2084,188 @@
          </div>
          <p>如果一个函数是奇函数或偶函数，那么就称这个函数具有<b>奇偶性</b>.否则，函数不具有奇偶性.</p>
          <p><span class="zt-ls"><b>例7</b></span>　判断下列函数的奇偶性.</p>
          <p>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>；（2） <math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mo>−</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>；</p>
          <p>（3） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；（4）<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mfrac>
                <mn>1</mn>
                <mrow>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>1</mn>
                </mrow>
              </mfrac>
            </math>.</p>
          <p><span class="zt-ls"><b>解</b></span>（1）
            <i>f</i>（<i>x</i>）的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
          <p class="p-btn" >
            <span>（1） <i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>；</span>
            <span class="btn-box" @click="isShowAnswer29 = !isShowAnswer29">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>4</sup>=<i>x</i><sup>4</sup>=<i>f</i>（<i>x</i>），</p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>是偶函数.</p>
          <p>（2）
            要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，
            且</p>
          <math display="block">
            <mi>f</mi>
            <mo stretchy="false">(</mo>
            <mo>−</mo>
            <mi>x</mi>
            <mo stretchy="false">)</mo>
            <mo>=</mo>
            <mo>−</mo>
            <mi>x</mi>
            <mo>−</mo>
            <mfrac>
              <mn>1</mn>
              <mrow>
          <div v-if="isShowAnswer29" >
            <p><span class="zt-ls"><b>解</b></span>（1）
              <i>f</i>（<i>x</i>）的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
            </p>
            <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>4</sup>=<i>x</i><sup>4</sup>=<i>f</i>（<i>x</i>），</p>
            <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>4</sup>是偶函数.</p>
          </div>
          <p class="p-btn">
            <span>
              （2） <math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mo>−</mo>
                <mi>x</mi>
              </mrow>
            </mfrac>
            <mo>=</mo>
            <mo>−</mo>
            <mi>x</mi>
            <mo>+</mo>
            <mfrac>
              <mn>1</mn>
                <mo>−</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
              </math>；
            </span>
            <span class="btn-box" @click="isShowAnswer30 = !isShowAnswer30">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer30" >
            <p>
              <span class="zt-ls"><b>解</b></span>（2）
              要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠0}，对任意<i>x</i>∈<i>D</i>，都有-<i>x</i>∈<i>D</i>，
              且</p>
            <math display="block">
              <mi>f</mi>
              <mo stretchy="false">(</mo>
              <mo>−</mo>
              <mi>x</mi>
            </mfrac>
            <mo>=</mo>
            <mo>−</mo>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mo stretchy="false">)</mo>
              <mo>=</mo>
              <mo>−</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>=</mo>
            <mo>−</mo>
            <mi>f</mi>
            <mo stretchy="false">(</mo>
            <mi>x</mi>
            <mo stretchy="false">)</mo>
            <mo>,</mo>
          </math>
          <p>所以，函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
            </math>是奇函数.</p>
          <p>（3）
            函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
          </p>
          <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>+（-<i>x</i>）=<i>x</i><sup>2</sup>-<i>x</i>，</p>
          <p>但　<i>f</i>（-<i>x</i>）≠<i>f</i>（<i>x</i>），且<i>f</i>（-<i>x</i>）≠-<i>f</i>（<i>x</i>），</p>
          <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>既不是奇函数，也不是偶函数.</p>
          <p>（4）
            要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>-1≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠1}，对任意<i>x</i>∈<i>D</i>，不都有-<i>x</i>∈<i>D</i>成立.
          </p>
          <p>所以，函数<math display="0">
              <mi>f</mi>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mfrac>
                <mn>1</mn>
                <mrow>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>1</mn>
                  <mi>x</mi>
                </mrow>
              </mfrac>
            </math>不具有奇偶性，它既不是奇函数也不是偶函数.</p>
              <mo>=</mo>
              <mo>−</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mfrac>
                <mn>1</mn>
                <mi>x</mi>
              </mfrac>
              <mo>=</mo>
              <mo>−</mo>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>x</mi>
                <mo>−</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
              <mo>=</mo>
              <mo>−</mo>
              <mi>f</mi>
              <mo stretchy="false">(</mo>
              <mi>x</mi>
              <mo stretchy="false">)</mo>
              <mo>,</mo>
            </math>
            <p>所以，函数<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mi>x</mi>
                <mo>−</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>x</mi>
                </mfrac>
              </math>是奇函数.
            </p>
          </div>
          <p class="p-btn">
            <span>
              （3） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；
            </span>
            <span class="btn-box" @click="isShowAnswer31 = !isShowAnswer31">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer31" >
            <p> <span class="zt-ls"><b>解</b></span>（3）
              函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，且
            </p>
            <p class="center"><i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>+（-<i>x</i>）=<i>x</i><sup>2</sup>-<i>x</i>，</p>
            <p>但　<i>f</i>（-<i>x</i>）≠<i>f</i>（<i>x</i>），且<i>f</i>（-<i>x</i>）≠-<i>f</i>（<i>x</i>），</p>
            <p>所以，函数<i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>既不是奇函数，也不是偶函数.</p>
          </div>
          <p class="p-btn" >
            <span>
              （4）<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mfrac>
                  <mn>1</mn>
                  <mrow>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>1</mn>
                  </mrow>
                </mfrac>
              </math>.
            </span>
            <span class="btn-box" @click="isShowAnswer32 = !isShowAnswer32">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer32" >
            <p> <span class="zt-ls"><b>解</b></span>（4）
              要使函数<i>f</i>（<i>x</i>）有意义，必须满足<i>x</i>-1≠0，所以函数<i>f</i>（<i>x</i>）的定义域是<i>D</i>={<i>x</i>|<i>x</i>≠1}，对任意<i>x</i>∈<i>D</i>，不都有-<i>x</i>∈<i>D</i>成立.
            </p>
            <p>所以，函数<math display="0">
                <mi>f</mi>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mfrac>
                  <mn>1</mn>
                  <mrow>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>1</mn>
                  </mrow>
                </mfrac>
              </math>不具有奇偶性，它既不是奇函数也不是偶函数.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
@@ -1921,101 +2334,147 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例1</b></span>　住在A城的小李早晨8：00出发，驾驶小轿车从A城以80 km/h 的速度到200 km处的B城，他在B城停留了3 h 后，再以100
            km/h的速度返回A城.在不考虑堵车等其他因素的情况下，设小李从A城出发<i>x</i>（h）后，小李与A城的距离是<i>y</i>（km）.</p>
          <p>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</p>
          <p>（2） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像；</p>
          <p>（3） 小李在返回A城途中，15：00刚好接到家人的电话，这时他距离A城多少千米？</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　首先求出小李从A城到B城和从B城返回A城共花费的时间，明确函数的定义域.小李去B城和返回A城的过程中，<i>y</i>与<i>x</i>分别对应的解析式不相同，所以该函数需用分段函数表示.
          <p>
            <span>
              <span class="zt-ls">
              <b>例1</b></span>　住在A城的小李早晨8：00出发，驾驶小轿车从A城以80 km/h 的速度到200 km处的B城，他在B城停留了3 h 后，再以100
              km/h的速度返回A城.在不考虑堵车等其他因素的情况下，设小李从A城出发<i>x</i>（h）后，小李与A城的距离是<i>y</i>（km）.
            </span>
            <span class="btn-box" @click="openDialog(thinkFive)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>解</b></span>（1） 小李从A城出发到B 城用时<math display="0">
              <mfrac>
                <mn>200</mn>
                <mn>80</mn>
              </mfrac>
              <mo>=</mo>
              <mn>2.5</mn>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>h</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，<i>x</i>的取值范围是{<i>x</i>|0＜<i>x</i>≤2.5}，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=80<i>x</i>；</p>
          <p>小李到B城后停留3 h，x的取值范围是{<i>x</i>|2.5＜<i>x</i>≤5.5}，对应关系是<i>y</i>=200；</p>
          <p>小李从<i>B</i>城返回<i>A</i>城用时<math display="0">
              <mfrac>
                <mn>200</mn>
                <mn>100</mn>
              </mfrac>
              <mo>=</mo>
              <mn>2</mn>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mi>h</mi>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，<i>x</i>的取值范围是{<i>x</i>|5.5＜<i>x</i>≤7.5}，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=200-100（<i>x</i>-5.5），即<i>y</i>=-100<i>x</i>+750.
          <p class="p-btn" >
            <span>
              （1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；
            </span>
            <span class="btn-box" @click="isShowAnswer33 = !isShowAnswer33">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>因此，用解析法将函数<i>f</i>（<i>x</i>）表示为<math display="0">
              <mi>y</mi>
              <mo>=</mo>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnalign="left left" columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mn>80</mn>
                      <mi>x</mi>
                      <mo>,</mo>
                    </mtd>
                    <mtd>
                      <mn>0</mn>
                      <mo>&lt;</mo>
                      <mi>x</mi>
                      <mo>⩽</mo>
                      <mn>2.5</mn>
                    </mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mn>200</mn>
                      <mo>,</mo>
                    </mtd>
                    <mtd>
                      <mn>2.5</mn>
                      <mo>&lt;</mo>
                      <mi>x</mi>
                      <mo>⩽</mo>
                      <mn>5.5</mn>
                      <mo>,</mo>
                    </mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mo>−</mo>
                      <mn>100</mn>
                      <mi>x</mi>
                      <mo>+</mo>
                      <mn>750</mn>
                      <mo>,</mo>
                      <mn>5.5</mn>
                      <mo>&lt;</mo>
                      <mi>x</mi>
                      <mo>⩽</mo>
                      <mn>7.5</mn>
                    </mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>.</p>
          <p>（2） 函数<i>y</i>=<i>f</i>（<i>x</i>）的图像如图3-24所示.</p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0111-4.jpg" /></p>
          <p class="img">图3-24</p>
          <p>（3） 小李从早晨8：00出发到15：00，共经过了7h，所以<i>x</i>=7，由（1） 中解析式得小李与<i>A</i>城的距离为</p>
          <p class="center">-100×7+750=50（km）.</p>
          <p>所以，小李返回A城途中接到家人电话时，距离A城刚好50 km.</p>
          <div v-if="isShowAnswer33" >
            <p><span class="zt-ls"><b>解</b></span>（1） 小李从A城出发到B 城用时<math display="0">
                <mfrac>
                  <mn>200</mn>
                  <mn>80</mn>
                </mfrac>
                <mo>=</mo>
                <mn>2.5</mn>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>h</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，<i>x</i>的取值范围是{<i>x</i>|0＜<i>x</i>≤2.5}，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=80<i>x</i>；</p>
            <p>小李到B城后停留3 h，x的取值范围是{<i>x</i>|2.5＜<i>x</i>≤5.5}，对应关系是<i>y</i>=200；</p>
            <p>小李从<i>B</i>城返回<i>A</i>城用时<math display="0">
                <mfrac>
                  <mn>200</mn>
                  <mn>100</mn>
                </mfrac>
                <mo>=</mo>
                <mn>2</mn>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mi>h</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，<i>x</i>的取值范围是{<i>x</i>|5.5＜<i>x</i>≤7.5}，<i>y</i>与<i>x</i>的对应关系是<i>y</i>=200-100（<i>x</i>-5.5），即<i>y</i>=-100<i>x</i>+750.
            </p>
            <p>因此，用解析法将函数<i>f</i>（<i>x</i>）表示为<math display="0">
                <mi>y</mi>
                <mo>=</mo>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnalign="left left" columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mn>80</mn>
                        <mi>x</mi>
                        <mo>,</mo>
                      </mtd>
                      <mtd>
                        <mn>0</mn>
                        <mo>&lt;</mo>
                        <mi>x</mi>
                        <mo>⩽</mo>
                        <mn>2.5</mn>
                      </mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>200</mn>
                        <mo>,</mo>
                      </mtd>
                      <mtd>
                        <mn>2.5</mn>
                        <mo>&lt;</mo>
                        <mi>x</mi>
                        <mo>⩽</mo>
                        <mn>5.5</mn>
                        <mo>,</mo>
                      </mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mo>−</mo>
                        <mn>100</mn>
                        <mi>x</mi>
                        <mo>+</mo>
                        <mn>750</mn>
                        <mo>,</mo>
                        <mn>5.5</mn>
                        <mo>&lt;</mo>
                        <mi>x</mi>
                        <mo>⩽</mo>
                        <mn>7.5</mn>
                      </mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>.
            </p>
          </div>
          <p class="p-btn" >
            <span>（2） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像；</span>
            <span class="btn-box" @click="isShowAnswer34 = !isShowAnswer34">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer34">
            <p> <span class="zt-ls"><b>解</b></span>（2） 函数<i>y</i>=<i>f</i>（<i>x</i>）的图像如图3-24所示.</p>
            <p class="center"><img class="img-f" alt="" src="../../assets/images/0111-4.jpg" /></p>
            <p class="img">图3-24</p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <p class="p-btn" >
            <span>（3） 小李在返回A城途中，15：00刚好接到家人的电话，这时他距离A城多少千米？</span>
            <span class="btn-box" @click="isShowAnswer35 = !isShowAnswer35">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer35" >
            <p> <span class="zt-ls"><b>解</b></span>（3） 小李从早晨8：00出发到15：00，共经过了7h，所以<i>x</i>=7，由（1） 中解析式得小李与<i>A</i>城的距离为</p>
            <p class="center">-100×7+750=50（km）.</p>
            <p>所以，小李返回A城途中接到家人电话时，距离A城刚好50 km.</p>
          </div>
        </div>
      </div>
    </div>
@@ -2031,56 +2490,192 @@
          </li>
        </ul>
        <div class="padding-116">
          <p><span class="zt-ls"><b>例2</b></span>　某农户要用6 000块砖建造三间面积相等的饲养室，如图3-25所示，其中<i>AB</i>，<i>AD</i>两面靠墙，每修筑长度1
            m的新墙需要砖200块.当<i>AB</i>为多少米时，修建的三间饲养室的总面积最大？最大面积是多少？</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例2</b></span>　某农户要用6 000块砖建造三间面积相等的饲养室，如图3-25所示，其中<i>AB</i>，<i>AD</i>两面靠墙，每修筑长度1
              m的新墙需要砖200块.当<i>AB</i>为多少米时，修建的三间饲养室的总面积最大？最大面积是多少？
            </span>
            <span class="btn-box" @click="openDialog(thinkSix)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
            <span class="btn-box" @click="isShowAnswer36 = !isShowAnswer36">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="center"><img class="img-f" alt="" src="../../assets/images/0112-1.jpg" /></p>
          <p class="img">图3-25</p>
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　首先需要计算备用材料可修建饲养室新墙的总长；因每间饲养室的周长是定值，所以设<i>AB</i>的长为<i>x</i>（m），就可以用含<i>x</i>的代数式表示<i>BC</i>的长；再用解析法表示总面积<i>y</i>（m<sup>2</sup>）与<i>x</i>（m）的函数关系；然后利用函数的性质来解决问题.
          <div v-if="isShowAnswer36" > 
            <p><span class="zt-ls"><b>解</b></span> 因为每修筑长度1 m的新墙需要砖200块，所以6 000块砖可以修筑新墙的总长度是6
              000÷200=30（m）.设<i>AB</i>为<i>x</i>（m），则<i>BC</i>为（30-3<i>x</i>）（m），三间饲养室的总面积为<i>y</i>（m<sup>2</sup>）.</p>
            <p>于是<i>y</i>=（30-3<i>x</i>）<i>x</i>，要有实际意义，必须满足<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mi>x</mi>
                        <mo>＞</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>30</mn>
                        <mo>−</mo>
                        <mn>3</mn>
                        <mi>x</mi>
                        <mo>＞</mo>
                        <mn>0</mn>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>.</p>
            <p>所以，<i>y</i>与<i>x</i>的函数关系是<i>y</i>=-3<i>x</i><sup>2</sup>+30<i>x</i>，0＜<i>x</i>＜10.</p>
            <p>整理得<i>y</i>=-3（<i>x</i>-5）<sup>2</sup>+75.</p>
            <p>所以，当<i>x</i>=5时，<i>y</i>值最大，最大值为75.</p>
            <p>即当<i>AB</i>为5 m时，三间饲养室的总面积最大，最大面积是75 m<sup>2</sup>.</p>
            <p>在实际生活中，很多与二次函数有关的最值问题都可通过分析、研究后，建立相应二次函数的数学模型，并运用二次函数的图像性质求最值.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例3</b></span>　某批发商购入一批30元/kg的绿色食品，若以40元/kg销售，则每月可批发销售400
              kg.由批发销售经验知道，每月销售量<i>y</i>（kg
              ）是销售单价<i>x</i>（元）的一次函数，其图像如图3-26所示.
            </span>
            <span class="btn-box" @click="openDialog(thinkSeven)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p><span class="zt-ls"><b>解</b></span> 因为每修筑长度1 m的新墙需要砖200块，所以6 000块砖可以修筑新墙的总长度是6
            000÷200=30（m）.设<i>AB</i>为<i>x</i>（m），则<i>BC</i>为（30-3<i>x</i>）（m），三间饲养室的总面积为<i>y</i>（m<sup>2</sup>）.</p>
          <p>于是<i>y</i>=（30-3<i>x</i>）<i>x</i>，要有实际意义，必须满足<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mi>x</mi>
                      <mo>＞</mo>
                      <mn>0</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mn>30</mn>
                      <mo>−</mo>
                      <mn>3</mn>
                      <mi>x</mi>
                      <mo>＞</mo>
                      <mn>0</mn>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>.</p>
          <p>所以，<i>y</i>与<i>x</i>的函数关系是<i>y</i>=-3<i>x</i><sup>2</sup>+30<i>x</i>，0＜<i>x</i>＜10.</p>
          <p>整理得<i>y</i>=-3（<i>x</i>-5）<sup>2</sup>+75.</p>
          <p>所以，当<i>x</i>=5时，<i>y</i>值最大，最大值为75.</p>
          <p>即当<i>AB</i>为5 m时，三间饲养室的总面积最大，最大面积是75 m<sup>2</sup>.</p>
          <p>在实际生活中，很多与二次函数有关的最值问题都可通过分析、研究后，建立相应二次函数的数学模型，并运用二次函数的图像性质求最值.</p>
          <p><span class="zt-ls"><b>例3</b></span>　某批发商购入一批30元/kg的绿色食品，若以40元/kg销售，则每月可批发销售400
            kg.由批发销售经验知道，每月销售量<i>y</i>（kg
            ）是销售单价<i>x</i>（元）的一次函数，其图像如图3-26所示.</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0112-3.jpg" /></p>
          <p class="img"> 图3-26</p>
          <p>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</p>
          <p>（2） 该批发商不低于购入价进行销售，设该批发商每月销售这批绿色食品可获得利润为<i>w</i>元，用解析法表示函数<i>w</i>=<i>g</i>（<i>x</i>）；</p>
          <p>（3） 当销售单价为多少时，该批发商每月可获得最大利润？最大利润是多少？</p>
          <p class="p-btn">
            <span>（1） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</span>
            <span class="btn-box" @click="isShowAnswer38 = !isShowAnswer38">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer38" > 
            <p><span class="zt-ls"><b>解</b></span>（1） 设函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式是<i>y</i>=<i>kx</i>+<i>b</i>，则</p>
            <p><math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mn>40</mn>
                        <mi>k</mi>
                        <mo>+</mo>
                        <mi>b</mi>
                        <mo>=</mo>
                        <mn>400</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>50</mn>
                        <mi>k</mi>
                        <mo>+</mo>
                        <mi>b</mi>
                        <mo>=</mo>
                        <mn>200</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>，解得<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mi>k</mi>
                        <mo>=</mo>
                        <mo>−</mo>
                        <mn>20</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mi>b</mi>
                        <mo>=</mo>
                        <mn>1200.</mn>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math></p>
            <p>即<i>y</i>=-20<i>x</i>+1 200.</p>
            <p>根据题意，当30≤<i>x</i>≤60时，函数<i>y</i>=-20<i>x</i>+1 200才有实际意义.</p>
            <p>所以，函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式可表示为</p>
            <p class="center"><i>y</i>=-20<i>x</i>+1 200，30≤<i>x</i>≤60.</p>
          </div>
          <p class="p-btn">
            <span>
            （2） 该批发商不低于购入价进行销售，设该批发商每月销售这批绿色食品可获得利润为<i>w</i>元，用解析法表示函数<i>w</i>=<i>g</i>（<i>x</i>）；
            </span>
            <span class="btn-box" @click="isShowAnswer39 = !isShowAnswer39">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer39" > 
            <p> <span class="zt-ls"><b>解</b></span>（2） 由题意得，<i>w</i>=（<i>x</i>-30）<i>y</i></p>
            <p>　　　　　　　　=（<i>x</i>-30）（-20<i>x</i>+1 200）</p>
            <p>　　　　　　　　=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，</p>
            <p>所以，函数<i>w</i>=<i>g</i>（<i>x</i>）的解析式可表示为</p>
            <p class="center"><i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60.</p>
          </div>
          <p class="p-btn">
            <span>
            （3） 当销售单价为多少时，该批发商每月可获得最大利润？最大利润是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer40 = !isShowAnswer40">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer40" > 
            <p> <span class="zt-ls"><b>解</b></span>（3） 由（2） 知，<i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60，配方得</p>
            <p class="center"><i>w</i>=-20（<i>x</i>-45）<sup>2</sup>+4 500.</p>
            <p>所以，当<i>x</i>=45时，<i>w</i>的值最大，最大值是4 500.</p>
            <p>答：当销售单价为45元时，该批发商每月可获得最大利润，最大利润是4 500元.</p>
          </div>
        </div>
      </div>
    </div>
@@ -2093,80 +2688,6 @@
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <p class="block"><span
              class="zt-ls2"><b>分析</b></span>　先由图像求出一次函数的解析式，再根据每月所获利润=（销售单价-进价）×每月销售量，列出每月所获利润<i>w</i>与销售单价<i>x</i>的函数关系.
          </p>
          <p><span class="zt-ls"><b>解</b></span>（1） 设函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式是<i>y</i>=<i>kx</i>+<i>b</i>，则</p>
          <p><math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mn>40</mn>
                      <mi>k</mi>
                      <mo>+</mo>
                      <mi>b</mi>
                      <mo>=</mo>
                      <mn>400</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mn>50</mn>
                      <mi>k</mi>
                      <mo>+</mo>
                      <mi>b</mi>
                      <mo>=</mo>
                      <mn>200</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math>，解得<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mtable columnspacing="1em" rowspacing="4pt">
                  <mtr>
                    <mtd>
                      <mi>k</mi>
                      <mo>=</mo>
                      <mo>−</mo>
                      <mn>20</mn>
                      <mo>，</mo>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                  <mtr>
                    <mtd>
                      <mi>b</mi>
                      <mo>=</mo>
                      <mn>1200.</mn>
                    </mtd>
                    <mtd></mtd>
                  </mtr>
                </mtable>
                <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
              </mrow>
            </math></p>
          <p>即<i>y</i>=-20<i>x</i>+1 200.</p>
          <p>根据题意，当30≤<i>x</i>≤60时，函数<i>y</i>=-20<i>x</i>+1 200才有实际意义.</p>
          <p>所以，函数<i>y</i>=<i>f</i>（<i>x</i>）的解析式可表示为</p>
          <p class="center"><i>y</i>=-20<i>x</i>+1 200，30≤<i>x</i>≤60.</p>
          <p>（2） 由题意得，<i>w</i>=（<i>x</i>-30）<i>y</i></p>
          <p>　　　　　　　　=（<i>x</i>-30）（-20<i>x</i>+1 200）</p>
          <p>　　　　　　　　=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，</p>
          <p>所以，函数<i>w</i>=<i>g</i>（<i>x</i>）的解析式可表示为</p>
          <p class="center"><i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60.</p>
          <p>（3） 由（2） 知，<i>w</i>=-20<i>x</i><sup>2</sup>+1 800<i>x</i>-36 000，30≤<i>x</i>≤60，配方得</p>
          <p class="center"><i>w</i>=-20（<i>x</i>-45）<sup>2</sup>+4 500.</p>
          <p>所以，当<i>x</i>=45时，<i>w</i>的值最大，最大值是4 500.</p>
          <p>答：当销售单价为45元时，该批发商每月可获得最大利润，最大利润是4 500元.</p>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[110]" :hideCollect="true" sourceType="json"
@@ -2308,7 +2829,7 @@
    <!-- 112 -->
    <div class="page-box hidePage" page="119">
    </div>
        <!-- 函数控件弹窗 -->
    <!-- 函数控件弹窗 -->
    <el-dialog :visible.sync="dialogVisible" width="60%" :append-to-body="true" :show-close="false">
      <div slot="title" style="padding: 0 0 15px 0;position: relative;">
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="dialogVisible = false" t="1718596022986"
@@ -2325,9 +2846,11 @@
      <iframe src="https://www.geogebra.org/calculator" frameborder="0" style="width: 100%; min-height: 800px"></iframe>
    </el-dialog>
    <!-- 解题思路弹窗 -->
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false">
      <div slot="title" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 解题思路 </span>
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
      @close="closeDialog" class="thinkDialog">
      <div slot="title" class="think-header"
        style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 分析 </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
@@ -2340,8 +2863,8 @@
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in thinkOne" :key="index">
          <div v-if="item.isShow" style="display: flex">
        <li v-for="(item, index) in thinkData" :key="index">
          <div v-if="index <= showIndex" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
@@ -2349,67 +2872,17 @@
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p">{{ item.txt }}</p>
            <p class="txt-p" v-html="item"></p>
          </div>
        </li>
      </ul>
      <div @click="showNext(thinkIndex)" style="
      <div @click="changeNext" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="thinkIndex != 3" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
            d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
            fill="#1296db" p-id="5068" />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db" p-id="5069" />
        </svg>
      </div>
    </el-dialog>
    <!-- 解题步骤弹窗 -->
    <el-dialog class="stepDialog" title="解题步骤" :visible.sync="stepDialog" width="40%" :append-to-body="true"
      :show-close="false">
      <div slot="title" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span>
          解题步骤
        </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="stepDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797" p-id="4253"></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797" p-id="4254"></path>
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in stepOne" :key="index">
          <div v-if="item.isShow" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
                v-if="index < stepOne.length - 1" />
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == stepOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p">{{ item.txt }}</p>
          </div>
        </li>
      </ul>
      <div @click="showNextChange(stepIndex)" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="stepIndex != 2" />
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
@@ -2429,6 +2902,14 @@
import examinations from '@/components/examinations/index.vue'
import { getResourcePath } from "@/assets/methods/resources";
import { getCollectResource, setCollectResource } from "@/assets/methods/resources";
const handleShow = (num) => {
  const obj = {}
  for (let index = 0; index < num; index++) {
    obj['isShowAnswer' + index] = false
  }
  return obj
}
const showObj = handleShow(50)
export default {
  name: '',
  props: {
@@ -2443,6 +2924,7 @@
  components: {examinations,paint},
  data() {
    return {
      ...showObj,
      collectImg: require("../../assets/images/icon/heart.png"),
      collectCheck: require("../../assets/images/icon/heart-check.png"),
      isShowExampleOne: false,
@@ -2452,7 +2934,6 @@
      isShowExampleFive: false,
      dialogVisible: false,
      thinkingDialog: false,
      stepDialog: false,
      videoPath: "",
      stepIndex: 1,
      thinkIndex: 1,
@@ -2463,103 +2944,32 @@
        txtOne: "",
        txtTwo: "",
      },
      showIndex:0,
      thinkData:[],
      thinkOne: [
        {
          txt: "1:一个函数是不 是偶函数,可以由 函数的图像是否关 于y 轴 对 称 来 判 断;当函数用解析 法表示时,可以用 偶 函 数 的 定 义 来 判断。 偶函数:一般地，设函数f(x)的定义域为D，如果对于任意xED，都有XED，且f(-x)=f(x)，那么函数f(x)就叫作偶函数",
          isShow: true,
        },
        {
          txt: "2:计算f(-x)",
          isShow: false,
        },
        {
          txt: "3:判断f(-x)是否等于f(x)",
          isShow: false,
        },
        "1:一个函数是不 是偶函数,可以由 函数的图像是否关 于y 轴 对 称 来 判 断;当函数用解析 法表示时,可以用 偶 函 数 的 定 义 来 判断。 偶函数:一般地，设函数f(x)的定义域为D，如果对于任意xED，都有XED，且f(-x)=f(x)，那么函数f(x)就叫作偶函数",
        "2:计算f(-x)",
        "3:判断f(-x)是否等于f(x)",
      ],
      stepOne: [
        {
          txt: "1:(1)函数f(x)=3x2+1的定义域是R，对任意XER，都有-XER",
          isShow: true,
        },
        {
          txt: "2:f(-x)=3(-x)2+1=3x2+1=f(x)",
          isShow: false,
        },
      thinkTwo:[
        '因为<i>AB</i>的长度为<i>x</i>（m），<i>BC</i>的长度为（12-<i>x</i>）（m），所以必须满足<i>x</i>＞0且12-<i>x</i>＞0才有实际意义.'
      ],
      dragQuestion: [
        {
          analysisCon: null,
          answer: ['A', 'B', 'C'],
          difficulty: 0,
          id: "7BC7B760",
          isCollect: false,
          isComplete: false,
          isRight: null,
          isUnfold: "",
          isUserAnswer: false,
          number: 1,
          option: [
            {
              img: "",
              index: "010311",
              txt: "胆小的",
              value: "A",
              isShow: true
            },
            {
              img: "",
              index: "010312",
              txt: "善良的",
              value: "B",
              isShow: true
            },
            {
              img: "",
              index: "010313",
              txt: "沉稳的",
              value: "C",
              isShow: true
            },
          ],
          optionStyle: "Txt",
          questionType: "drag",
          score: 2,
          stem: {
            0: "蚂蚁队长走路昂首挺胸、步伐坚定，它是一只(",
            1: {
              data: "span",
              num: 0
            },
            2: ")蚂蚁;小蚂蚁走起路来小心翼翼，眼神飘忽不定，它是一只(",
            3: {
              data: "span",
              num: 1
            },
            4: ")蚂蚁;蚂蚁小妹面带微笑，时刻愿意帮助大家，它是一只(",
            5: {
              data: "span",
              num: 2,
            },
            6: " )蚂蚁"
          },
          stemStyle: "RichTxt",
          type: "拖拽题",
          userAnswer: [
            {
              vlaue: '',
              txt: ''
            },
            {
              vlaue: '',
              txt: ''
            },
            {
              vlaue: '',
              txt: ''
            },
          ]
        },
      thinkThree:[
        '计算该军舰从出发地驶入海港所需要的时间，就可得到函数<i>s</i>=<i>f</i>（<i>t</i>）的定义域.用解析法表示函数后，再画出函数的图像.'
      ],
      thinkFour:[
        '首先需明确这个函数的定义域.由于居民用电量不同，其收费标准也不同，所以这是分段函数.其次要厘清自变量<i>x</i>在不同的取值范围内与因变量<i>y</i>之间的对应关系，并列出相应的解析式来解决相关问题.'
      ],
      thinkFive:[
        '首先求出小李从A城到B城和从B城返回A城共花费的时间，明确函数的定义域.小李去B城和返回A城的过程中，<i>y</i>与<i>x</i>分别对应的解析式不相同，所以该函数需用分段函数表示.'
      ],
      thinkSix:[
        '首先需要计算备用材料可修建饲养室新墙的总长；因每间饲养室的周长是定值，所以设<i>AB</i>的长为<i>x</i>（m），就可以用含<i>x</i>的代数式表示<i>BC</i>的长；',
        '再用解析法表示总面积<i>y</i>（m<sup>2</sup>）与<i>x</i>（m）的函数关系；然后利用函数的性质来解决问题.'
      ],
      thinkSeven:[
        '先由图像求出一次函数的解析式，',
        '再根据每月所获利润=（销售单价-进价）×每月销售量，列出每月所获利润<i>w</i>与销售单价<i>x</i>的函数关系.'
      ]
    };
  },
@@ -2592,25 +3002,18 @@
      }
      this.handleChapterData();
    },
        openMathDiaolog() {
    openMathDiaolog() {
      this.dialogVisible = true;
    },
    openThinkingDialog() {
      this.thinkingDialog = true;
    openDialog(queryData) {
      this.thinkData = queryData
      this.thinkingDialog = !this.thinkingDialog
    },
    showNext(num) {
      const number = this.thinkOne.findIndex((item, index) => index == num);
      this.thinkOne[number].isShow = true;
      if (this.thinkIndex <= 2) {
        this.thinkIndex++;
      }
    closeDialog() {
      this.showIndex = 0
    },
    showNextChange(num) {
      const number = this.stepOne.findIndex((item, index) => index == num);
      this.stepOne[number].isShow = true;
      if (this.stepIndex < 2) {
        this.stepIndex++;
      }
    changeNext() {
      if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
    },
    //资源收藏事件
    handleCollectResource(id, md5, resourcePath, resourceType, source, resourceName) {
@@ -2636,14 +3039,6 @@
</script>

<style lang="less" scoped>
  
.iframe-box {
  width: 100%;
  min-height: 800px;
  border: 1px solid #00a1e9;
  border-radius: 10px;
}

li {
  list-style: none;
}

 src/books/mathBook/view/components/chapter004.vue

Diff too large

 src/books/mathBook/view/components/chapter005.vue

Diff too large

 src/books/mathBook/view/components/header.vue

@@ -1,5 +1,5 @@
<template>
  <div class="chapter" num="0">
  <div class="chapter" num="1">
    <!-- 封面1 -->
    <div class="page-box cover mt-20" page="1">
      <div v-if="showPageList.indexOf(1) > -1">

 src/books/mathBook/view/components/index.vue

@@ -3,23 +3,48 @@
    <div id="searchDomBox" style="display: none">
      <div id="searchContent"></div>
    </div>
    <div class="page-content" :style="{
      fontSize: fontSize ? fontSize + 'px' : '16px',
      transform: `scale(${pageZoom ? pageZoom : 1})`,
      transformOrigin: 'center top',
    }">
      <pageHeader v-if="showCatalogList.indexOf(0) > -1" :showPageList="loadPageList"></pageHeader>
      <chapterOne v-if="showCatalogList.indexOf(1) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
    <div
      class="page-content"
      :style="{
        fontSize: fontSize ? fontSize + 'px' : '16px',
        transform: `scale(${pageZoom ? pageZoom : 1})`,
        transformOrigin: 'center top',
      }"
    >
      <pageHeader
        v-if="showCatalogList.indexOf(1) > -1"
        :showPageList="loadPageList"
      ></pageHeader>
      <chapterOne
        v-if="showCatalogList.indexOf(2) > -1"
        :showPageList="loadPageList"
        :questionData="questionDataMap"
      >
      </chapterOne>
      <chapterTwo v-if="showCatalogList.indexOf(3) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
      <chapterTwo
        v-if="showCatalogList.indexOf(3) > -1"
        :showPageList="loadPageList"
        :questionData="questionDataMap"
      >
      </chapterTwo>
      <chapterThree v-if="showCatalogList.indexOf(4) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
      <chapterThree
        v-if="showCatalogList.indexOf(4) > -1"
        :showPageList="loadPageList"
        :questionData="questionDataMap"
      >
      </chapterThree>
      <chapterFour v-if="showCatalogList.indexOf(5) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
      <chapterFour
        v-if="showCatalogList.indexOf(5) > -1"
        :showPageList="loadPageList"
        :questionData="questionDataMap"
      >
      </chapterFour>
      <chapterFive v-if="showCatalogList.indexOf(6) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
      <chapterFive
        v-if="showCatalogList.indexOf(6) > -1"
        :showPageList="loadPageList"
        :questionData="questionDataMap"
      >
      </chapterFive>

    </div>
  </div>
</template>
@@ -30,8 +55,8 @@
import chapterOne from "./chapter001.vue";
import chapterTwo from "./chapter002.vue";
import chapterThree from "./chapter003.vue";
import chapterFour from './chapter004.vue'
import chapterFive from './chapter005.vue'
import chapterFour from "./chapter004.vue";
import chapterFive from "./chapter005.vue";
import NoteIcon from "@/assets/images/biji.png";
import _ from "lodash";
import Swiper from "swiper/bundle";
@@ -57,6 +82,8 @@
      highlightData: null,
      questionId: {},
      collectId: [],
      questionDataIndex: 0, // 当前请求的是哪个章节的题目
      questionList: [], // 章节题目列表
    };
  },
  computed: {
@@ -105,7 +132,7 @@
  },
  mounted() {
    // 默认加载章节
    this.showCatalogList = [0];
    this.showCatalogList = [1];
    // 滚动监听节流
    this.throttledScrollHandler = _.throttle(
      this.scrollFun,
@@ -161,8 +188,8 @@
    }, 500);

    // 测试页面跳转
    setTimeout(() => {
      this.gotoPage(3, 111);
    // setTimeout(() => {
    //   this.gotoPage(6,206);
    //   //   setTimeout(() => {
    //   //     this.renderSign("Highlight", {
    //   //       id: "2ACA9359",
@@ -190,11 +217,11 @@
    //   //   txt: " 运动系统是由骨、骨连结和骨骼肌三部分组成的。全身的骨通过骨连结组成人体骨骼（见图1-1）。骨骼是人体的支架，具有保护内脏器官、供肌肉附着和作为肌肉运动的杠杆等作用。在神经系统的支配下，肌肉收缩牵动所附着的骨绕着关节转动，使身体产生各种动作。所以，运动系统具有运动、支持和保护等功能，幼年时期的骨骼还具有造血功能。 ",
    //   //   txtIndex: 57
    //   // });
    }, 500);
    // }, 500);

    // 获取题目id列表
    this.getQuestionId();
    this.getCollect()
    this.getCollect();
  },
  methods: {
    // setZoom1() {
@@ -213,8 +240,7 @@
    // },
    // 滚动监听
    scrollFun(event) {

      this.handleVideoPicture()
      this.handleVideoPicture();

      // 判断向上滚动还是向下滚动
      if (event.target.scrollTop > this.previousScrollTop) {
@@ -270,7 +296,6 @@
            this.catalogLength - 2,
            this.catalogLength - 1,
            this.catalogLength,

          ];
        } else {
          this.showCatalogList = [catalog - 1, catalog, catalog + 1];
@@ -455,8 +480,8 @@
          page && pageThemeColor && pageThemeColor[page]
            ? pageThemeColor[page]
            : chapterNum && chapterThemeColor && chapterThemeColor[chapterNum]
              ? chapterThemeColor[chapterNum]
              : bookThemeColor;
            ? chapterThemeColor[chapterNum]
            : bookThemeColor;
        if (themeColor) {
          domItem.style.color = themeColor;
        }
@@ -473,8 +498,8 @@
          page && pageThemeColor && pageThemeColor[page]
            ? pageThemeColor[page]
            : chapterNum && chapterThemeColor && chapterThemeColor[chapterNum]
              ? chapterThemeColor[chapterNum]
              : bookThemeColor;
            ? chapterThemeColor[chapterNum]
            : bookThemeColor;
        if (themeColor) {
          domItem.style.backgroundColor = themeColor;
        }
@@ -491,8 +516,8 @@
          page && pageThemeColor && pageThemeColor[page]
            ? pageThemeColor[page]
            : chapterNum && chapterThemeColor && chapterThemeColor[chapterNum]
              ? chapterThemeColor[chapterNum]
              : bookThemeColor;
            ? chapterThemeColor[chapterNum]
            : bookThemeColor;
        if (themeColor) {
          domItem.style.borderColor = themeColor;
        }
@@ -554,17 +579,21 @@
            if (!this.questionDataMap[page]) {
              if (this.questionId && this.questionId[catalog]) {
                if (this.questionId[catalog][page]) {
                  console.log(page,Array.isArray(this.questionId[catalog][page]));
                  if(Array.isArray(this.questionId[catalog][page])) {
                    this.questionDataMap[page] = await this.getQuestion(catalog, page,false);
                  if (Array.isArray(this.questionId[catalog][page])) {
                    this.questionDataMap[page] = await this.getQuestion(
                      catalog,
                      page,
                      false
                    );
                  } else {
                    const obj = {}
                    const obj = {};
                    for (let key in this.questionId[catalog][page]) {
                      obj[key] = await this.getQuestion(catalog, page,key)
                      obj[key] = await this.getQuestion(catalog, page, key);
                    }
                    this.questionDataMap[page] = obj
                    this.questionDataMap[page] = obj;
                  }
                }
                console.log(1, this.questionDataMap);
              }
            }
            // 渲染这一页的标记
@@ -814,7 +843,7 @@
      // 记录高亮信息
      this.highlightData = data;
      // 跳转
      this.gotoPage(data.catalog, data.page, () => { });
      this.gotoPage(data.catalog, data.page, () => {});
    },
    // 获取题目列表
    getQuestionId() {
@@ -826,7 +855,7 @@
    },
    // 获取题目收藏id列表
    getCollect() {
      if(!localStorage.getItem(this.config.tokenKey)) return false
      if (!localStorage.getItem(this.config.tokenKey)) return false;
      this.MG.identity
        .getUserKey({
          domain: "collectData",
@@ -836,17 +865,20 @@
          try {
            const collect = JSON.parse(res[0].value);
            if (collect.length) {
              this.collectId = collect.find(item => item.type == 'json').collectList
              this.collectId = collect.find(
                (item) => item.type == "json"
              ).collectList;
            }
          } catch (error) {
            console.log("暂无数据");
          }
        }).catch(res => {
          console.log('index 请求题目收藏id报错');
        })
        .catch((res) => {
          console.log("index 请求题目收藏id报错");
        });
    },
    // 获取章节题目
    async getQuestion(num, page,questionIndex) {
    async getQuestion(num, page, questionIndex) {
      let cardList = [
        {
          catalogName: "单选题",
@@ -871,40 +903,57 @@
      ];
      if (this.questionId) {
        if (this.questionId[num] && this.questionId[num][page]) {
          const res = await axios.get(
            this.config.activeBook.resourceUrl + "/question-" + num + ".json"
          );
          if (!res.data) return [];
          let ids = []
          questionIndex ? ids = this.questionId[num][page][questionIndex] : ids = this.questionId[num][page]
          for (let index = 0; index < res.data.data.length; index++) {
            const item = res.data.data[index];
          if (num != this.questionDataIndex) {
            // 判断当前章节的题目json是否已经请求过
            const res = await axios.get(
              this.config.activeBook.resourceUrl + "/question-" + num + ".json"
            );
            if (!res.data) return [];
            this.questionList = res.data.data;
            this.questionDataIndex = res.data.chapterNum;
            console.log("章节号", num, res);
          }
          let ids = [];
          questionIndex
            ? (ids = this.questionId[num][page][questionIndex])
            : (ids = this.questionId[num][page]);
          for (let index = 0; index < this.questionList.length; index++) {
            const item = this.questionList[index];
            // 数学公式加类名去修改样式
            if (item.type && item.type == 'material') {
              if (!item.infoList.length) return false
              item.infoList.forEach(citem => {
                if (citem.answer) citem.answer = citem.answer.replace(/\<math/gi, '<math class="examination-math"')
              })
            if (item.type && item.type == "material") {
              if (!item.infoList.length) return false;
              item.infoList.forEach((citem) => {
                if (citem.answer)
                  citem.answer = citem.answer.replace(
                    /\<math/gi,
                    '<math class="examination-math"'
                  );
              });
            } else {
              if (item.answer) item.answer = item.answer.replace(/\<math/gi, '<math class="examination-math"')
              if (item.answer)
                item.answer = item.answer.replace(
                  /\<math/gi,
                  '<math class="examination-math"'
                );
            }
            item.isCollect = this.collectId.indexOf(item.id) > -1 ? true : false
            item.isCollect =
              this.collectId.indexOf(item.id) > -1 ? true : false;
            if (ids.indexOf(item.id) > -1) {
              if (item.type && item.type == "material") {
                cardList.push(item);
              } else {
                if (item.questionType == "judge") {
                  cardList[1].infoList.push(item);
                }  
                }
                if (item.questionType == "singleChoice") {
                  cardList[0].infoList.push(item);
                } 
                 if (item.questionType == "multipleChoice") {
                }
                if (item.questionType == "multipleChoice") {
                  cardList[2].infoList.push(item);
                } 
                 if (item.questionType == "completion") {
                }
                if (item.questionType == "completion") {
                  cardList[3].infoList.push(item);
                } 
                }
                if (item.questionType == "shortAnswer") {
                  cardList[4].infoList.push(item);
                }
@@ -917,17 +966,14 @@
        return [];
      }
    },

    // 视频小窗
    handleVideoPicture() {
      let doms = (
        this.container ? this.container : document
      ).querySelectorAll(".video");
      doms = Array.from(doms)
      if (!doms.length) return false
      const playVudio = doms
        .reverse()
        .find((item) => item.paused == false);
      let doms = (this.container ? this.container : document).querySelectorAll(
        ".video"
      );
      doms = Array.from(doms);
      if (!doms.length) return false;
      const playVudio = doms.reverse().find((item) => item.paused == false);
      if (playVudio) {
        const bottomGap = playVudio.getBoundingClientRect().bottom;
        const topGap = playVudio.getBoundingClientRect().top;
@@ -935,7 +981,7 @@
          playVudio.requestPictureInPicture();
        }
      }
    }
    },
  },
  components: {
    pageHeader,

 src/components/calculator/index.vue

New file
@@ -0,0 +1,58 @@
<template>
  <div ref="ggbContainer" class="ggb-container"></div>
</template>

<script lang="ts">

export default {
  mounted() {
  if (!window.GGBApplet) {
      const script = document.createElement("script");
      script.src = "https://www.geogebra.org/apps/deployggb.js";
      script.onload = () => {
        this.initGeoGebra();
      };
      document.body.appendChild(script);
    } else {
      this.initGeoGebra();
    }
  },
  methods:{
    initGeoGebra() {
        var params = {
          id: "ggbApplet",
          appName: "scientific",
          width: 600,
          height: 600,
          showToolBar: true,
          borderColor: null,
          showMenuBar: true,
          allowStyleBar: true,
          showAlgebraInput: true,
          enableLabelDrags: false,
          enableShiftDragZoom: true,
          capturingThreshold: null,
          showToolBarHelp: false,
          errorDialogsActive: true,
          showTutorialLink: true,
          showLogging: true,
          useBrowserForJS: false,
        };

        if (this.$refs.ggbContainer) {
          const applet = new GGBApplet(params, true);
          applet.inject(this.$refs.ggbContainer);
        }
      }
  }
}

</script>

<style scoped>
.ggb-container {
  width: 100%;
  height: 100%;
  /* 其他样式 */
}
</style>

 src/components/examinations/index.vue

@@ -38,7 +38,7 @@
              <p
                class="titleText text-fl"
                v-if="
                  value.stemStyle == 'Txt' && value.questionType != 'completion'
                  value.stemStyle == 'Txt' && value.questionType != 'completion' &&  value.questionType !='dropdown'
                "
                :id="value.id"
                v-html="value.stem.stemTxt"
@@ -73,6 +73,7 @@
                  <span
                    v-if="typeof itemText == 'string'"
                    v-html="itemText"
                    class="input-txt"
                  ></span>
                  <input
                    v-else
@@ -91,6 +92,33 @@
                v-html="value.stem.stemTxt"
                v-cloak
              ></p>
              <!-- 下拉选择题 -->
              <p class="titleText" v-if="value.questionType == 'dropdown'">
                <span
                  v-for="(itemText, indexText) in value.stem"
                  :key="indexText + 'questionType'"
                >
                  <span
                    v-if="typeof itemText == 'string'"
                    v-html="itemText"
                    class="input-txt"
                  ></span>
                  <el-select 
                    v-else 
                    v-model="value.userAnswer" 
                    :disabled="value.isComplete"
                  >
                    <el-option 
                      v-for="citem in value.option"
                      :key="citem.index"
                      :label="citem.txt"
                      :value="citem.value"
                    >

                    </el-option>
                  </el-select>
                </span>
              </p>
            </div>
            <img
              :src="value.isCollect ? isHeart : heart"
@@ -551,7 +579,6 @@
  watch: {
    cardList: {
      handler(newVal) {
        // console.log('新值',newVal);
        this.cardData = this.cardList;
        if (newVal && newVal.length) {
          this.loading = false;
@@ -566,6 +593,18 @@
    this.getErrorList();
  },
  methods: {
    // 获取不受保护的图片
    getPublicImage(md5, width, height) {
      if(!md5) return 
      if(md5.includes('http')) return md5
      let src = null;
      if (md5) {
        src = process.env.VUE_APP_API_URL + `/file/GetPreViewImage?md5=${md5}`;
      } 
      if (width) src += `&width=${width}`;
      if (height) src += `&height=${height}`;
      return src;
    },
    // 数组转为字符串方法
    arrayToString(data) {
      // 检查是否为数组
@@ -646,9 +685,9 @@
            }
          } else if (
            citem.questionType == "singleChoice" ||
            citem.questionType == "judge"
            citem.questionType == "judge" || 
            citem.questionType == 'dropdown'
          ) {
            if (citem.id == "63825") console.log("i", item);
            citem.isRight = citem.answer == citem.userAnswer;
          } else if (citem.questionType == "shortAnswer") {
            // 简答 翻译
@@ -858,6 +897,12 @@
</script>


<style lang="less" >
  .titleText img {
    max-width: 80%;
  }
</style>

<style lang="less" scoped>
.catalogName {
  text-indent: 1em !important;
@@ -1010,11 +1055,14 @@
      font-size: 16px;
      line-height: 32px;
      color: #000;

      .input-txt {
        display: flex;
        flex-wrap: wrap;
        align-items: center;
      }
      span {
        display: inline-block;
        font-size: 16px;
        // line-height: 26px;
        color: #000;
        font-weight: 400;
        margin-top: 6px;

			@@ -1,8 +1,8 @@
			VUE_APP_ENV = 'product'
			VUE_APP_API_URL = "https://jsek.bnuic.com"
			# VUE_APP_RESOURCE_CTX = 'https://jsek.bnuic.com/books/resource/'
			# VUE_APP_PUBLIC_PATH = 'https://jsek.bnuic.com/books/book/botany'
			VUE_APP_RESOURCE_CTX = 'http://182.92.203.7:3007/books/resource/'
			VUE_APP_PUBLIC_PATH = 'http://182.92.203.7:3007/books/book/botany'
			VUE_APP_RESOURCE_CTX = 'https://jsek.bnuic.com/books/resource/'
			VUE_APP_PUBLIC_PATH = 'https://jsek.bnuic.com/books/book/mathBook'
			# VUE_APP_RESOURCE_CTX = 'http://182.92.203.7:3007/books/resource/'
			# VUE_APP_PUBLIC_PATH = 'http://182.92.203.7:3007/books/book/botany'
			VUE_APP_BOOK_LIST = "childHealth/lifeCare/sportsAndHealth/embedded/english/artAndDance/artAndDrama/mathBook/botany"
			VUE_APP_BOOK_ID = 'botany'
			VUE_APP_BOOK_ID = 'mathBook'

			@@ -64,12 +64,11 @@
			// artAndDrama
			// mathBook
			// civilAviation

			this.activeBook = await this.config.getBookConfig(
			process.env.VUE_APP_RESOURCE_CTX +
			(process.env.VUE_APP_ENV == "product"
			? process.env.VUE_APP_BOOK_ID
			: "civilAviation")
			: "mathBook")
			);

			// this.activeBook = await this.config.getBookConfig(

			@@ -94,6 +94,7 @@
			// 默认加载章节
			this.showCatalogList = [1];
			// 滚动监听节流
			debugger
			this.throttledScrollHandler = _.throttle(
			this.scrollFun,
			this.throttleThreshold,
			@@ -198,6 +199,8 @@
			scrollFun(event) {
			this.handleVideoPicture()
			// 判断向上滚动还是向下滚动
			console.log(11);

			if (event.target.scrollTop > this.previousScrollTop) {
			this.getAduio();
			// 向下
			@@ -207,6 +210,9 @@
			currentScrollTop >=
			event.target.scrollHeight - this.loadThreshold
			) {
			console.log(1);

			debugger
			// 到达阈值
			if (
			this.showCatalogList[this.showCatalogList.length - 1] <

			@@ -430,7 +430,7 @@
			.page-box {
			position: relative;
			box-sizing: border-box;
			min-height: 1150px;
			min-height: 1120px;
			margin-bottom: 20px;
			box-shadow: 0 3px 6px 1px #00000029;
			background-color: #fff;
			@@ -557,6 +557,9 @@
			.t0 {
			text-indent: 0;
			}
			.t1 {
			text-indent: 1em;
			}
			.t- {
			text-indent: 0.5em;
			}
			@@ -580,7 +583,7 @@
			}
			.page-box {
			box-sizing: border-box;
			min-height: 1150px;
			min-height: 1120px;
			margin-bottom: 20px;
			box-shadow: 0 3px 6px 1px #00000029;
			background-color: #fff;
			@@ -701,6 +704,9 @@
			}
			.mt-40 {
			margin-top: 40px;
			}
			.mt-60 {
			margin-top: 60px !important;
			}
			.mt-80 {
			margin-top: 80px !important;
			@@ -854,6 +860,22 @@
			height: 0 !important;
			box-shadow: none !important;
			}
			// 带按钮p标签
			.p-btn {
			display: flex;
			justify-content: left;
			align-items: center;
			flex-wrap: wrap;
			i {
			text-indent: 0;
			}
			}
			.iframe-box {
			width: 100%;
			min-height: 800px;
			border: 1px solid #00a1e9;
			border-radius: 10px;
			}
			}

			/* 媒体查询做基础响应式布局 */

			@@ -1,5 +1,5 @@
			<template>
			<div class="chapter" num="1">
			<div class="chapter" num="2">
			<div class="page-box" page="8">
			<div v-if="showPageList.indexOf(8) > -1">
			<h1 id="a007">
			@@ -67,7 +67,7 @@
			</p>
			<p>（2） 0～10中的所有奇数；</p>
			<p>（3）我国农历二十四节气；</p>
			<p>（4）方程x2-5x-6=0的解；</p>
			<p>（4）方程<i>x</i><sup>2</sup>-5<i>x</i>-6=0的解；</p>
			<p>（5）到一个角的两边距离相等的所有点.</p>

			<p class="left">
			@@ -804,16 +804,14 @@
			</ul>
			<div class="padding-116">
			<div class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0023-1.jpg" style="margin-top: 30px" />
			<img class="img-b" alt="" src="../../assets/images/0023-1.jpg" style="margin-top: 30px" />
			<p class="img" style="font-size: 14px">图1-4</p>
			</div>

			<p>根据子集的定义，任何一个集合A都是它自身的子集，即A⊆A.</p>
			<p>
			我们规定：<b>空集是任何集合的子集</b>
			，即对于任何一个集合A，都有∅⊆A.
			</p>

			<div class="img-float openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0023-2.jpg" />
			<p class="img" style="font-size: 14px">图1-5</p>
			@@ -858,7 +856,6 @@
			</p>
			</li>
			</ul>

			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			@@ -2101,24 +2098,6 @@
			<!-- 030 -->
			<div class="page-box hidePage" page="37">
			</div>

			<!-- 函数控件弹窗 -->
			<el-dialog :visible.sync="dialogVisible" width="60%" :append-to-body="true" :show-close="false">
			<div slot="title" style="padding: 0 0 15px 0; position: relative">
			<svg style="position: absolute; right: 10px; cursor: pointer" @click="dialogVisible = false" t="1718596022986"
			class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
			height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
			<path
			d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
			fill="#979797" p-id="4253"></path>
			<path
			d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
			fill="#979797" p-id="4254"></path>
			</svg>
			</div>
			<iframe src="https://www.geogebra.org/calculator" frameborder="0" style="width: 100%; min-height: 800px"></iframe>
			</el-dialog>

			<!-- 解题思路弹窗 -->
			<el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false" @close="closeDialog" class="thinkDialog" >
			<div slot="title" class="think-header" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
			@@ -2248,7 +2227,6 @@
			},
			collectImg: require('../../assets/images/icon/heart.png'),
			collectCheck: require('../../assets/images/icon/heart-check.png'),
			dialogVisible: false,
			thinkingDialog: false,
			videoPath: '',
			stepIndex: 1,

			@@ -1,5 +1,5 @@
			<template>
			<div class="chapter" num="0">
			<div class="chapter" num="1">
			<!-- 封面1 -->
			<div class="page-box cover mt-20" page="1">
			<div v-if="showPageList.indexOf(1) > -1">

			@@ -3,23 +3,48 @@
			<div id="searchDomBox" style="display: none">
			<div id="searchContent"></div>
			</div>
			<div class="page-content" :style="{
			fontSize: fontSize ? fontSize + 'px' : '16px',
			transform: `scale(${pageZoom ? pageZoom : 1})`,
			transformOrigin: 'center top',
			}">
			<pageHeader v-if="showCatalogList.indexOf(0) > -1" :showPageList="loadPageList"></pageHeader>
			<chapterOne v-if="showCatalogList.indexOf(1) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
			<div
			class="page-content"
			:style="{
			fontSize: fontSize ? fontSize + 'px' : '16px',
			transform: `scale(${pageZoom ? pageZoom : 1})`,
			transformOrigin: 'center top',
			}"
			>
			<pageHeader
			v-if="showCatalogList.indexOf(1) > -1"
			:showPageList="loadPageList"
			></pageHeader>
			<chapterOne
			v-if="showCatalogList.indexOf(2) > -1"
			:showPageList="loadPageList"
			:questionData="questionDataMap"
			>
			</chapterOne>
			<chapterTwo v-if="showCatalogList.indexOf(3) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
			<chapterTwo
			v-if="showCatalogList.indexOf(3) > -1"
			:showPageList="loadPageList"
			:questionData="questionDataMap"
			>
			</chapterTwo>
			<chapterThree v-if="showCatalogList.indexOf(4) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
			<chapterThree
			v-if="showCatalogList.indexOf(4) > -1"
			:showPageList="loadPageList"
			:questionData="questionDataMap"
			>
			</chapterThree>
			<chapterFour v-if="showCatalogList.indexOf(5) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
			<chapterFour
			v-if="showCatalogList.indexOf(5) > -1"
			:showPageList="loadPageList"
			:questionData="questionDataMap"
			>
			</chapterFour>
			<chapterFive v-if="showCatalogList.indexOf(6) > -1" :showPageList="loadPageList" :questionData="questionDataMap">
			<chapterFive
			v-if="showCatalogList.indexOf(6) > -1"
			:showPageList="loadPageList"
			:questionData="questionDataMap"
			>
			</chapterFive>

			</div>
			</div>
			</template>
			@@ -30,8 +55,8 @@
			import chapterOne from "./chapter001.vue";
			import chapterTwo from "./chapter002.vue";
			import chapterThree from "./chapter003.vue";
			import chapterFour from './chapter004.vue'
			import chapterFive from './chapter005.vue'
			import chapterFour from "./chapter004.vue";
			import chapterFive from "./chapter005.vue";
			import NoteIcon from "@/assets/images/biji.png";
			import _ from "lodash";
			import Swiper from "swiper/bundle";
			@@ -57,6 +82,8 @@
			highlightData: null,
			questionId: {},
			collectId: [],
			questionDataIndex: 0, // 当前请求的是哪个章节的题目
			questionList: [], // 章节题目列表
			};
			},
			computed: {
			@@ -105,7 +132,7 @@
			},
			mounted() {
			// 默认加载章节
			this.showCatalogList = [0];
			this.showCatalogList = [1];
			// 滚动监听节流
			this.throttledScrollHandler = _.throttle(
			this.scrollFun,
			@@ -161,8 +188,8 @@
			}, 500);

			// 测试页面跳转
			setTimeout(() => {
			this.gotoPage(3, 111);
			// setTimeout(() => {
			// this.gotoPage(6,206);
			// // setTimeout(() => {
			// // this.renderSign("Highlight", {
			// // id: "2ACA9359",
			@@ -190,11 +217,11 @@
			// // txt: " 运动系统是由骨、骨连结和骨骼肌三部分组成的。全身的骨通过骨连结组成人体骨骼（见图1-1）。骨骼是人体的支架，具有保护内脏器官、供肌肉附着和作为肌肉运动的杠杆等作用。在神经系统的支配下，肌肉收缩牵动所附着的骨绕着关节转动，使身体产生各种动作。所以，运动系统具有运动、支持和保护等功能，幼年时期的骨骼还具有造血功能。 ",
			// // txtIndex: 57
			// // });
			}, 500);
			// }, 500);

			// 获取题目id列表
			this.getQuestionId();
			this.getCollect()
			this.getCollect();
			},
			methods: {
			// setZoom1() {
			@@ -213,8 +240,7 @@
			// },
			// 滚动监听
			scrollFun(event) {

			this.handleVideoPicture()
			this.handleVideoPicture();

			// 判断向上滚动还是向下滚动
			if (event.target.scrollTop > this.previousScrollTop) {
			@@ -270,7 +296,6 @@
			this.catalogLength - 2,
			this.catalogLength - 1,
			this.catalogLength,

			];
			} else {
			this.showCatalogList = [catalog - 1, catalog, catalog + 1];
			@@ -455,8 +480,8 @@
			page && pageThemeColor && pageThemeColor[page]
			? pageThemeColor[page]
			: chapterNum && chapterThemeColor && chapterThemeColor[chapterNum]
			? chapterThemeColor[chapterNum]
			: bookThemeColor;
			? chapterThemeColor[chapterNum]
			: bookThemeColor;
			if (themeColor) {
			domItem.style.color = themeColor;
			}
			@@ -473,8 +498,8 @@
			page && pageThemeColor && pageThemeColor[page]
			? pageThemeColor[page]
			: chapterNum && chapterThemeColor && chapterThemeColor[chapterNum]
			? chapterThemeColor[chapterNum]
			: bookThemeColor;
			? chapterThemeColor[chapterNum]
			: bookThemeColor;
			if (themeColor) {
			domItem.style.backgroundColor = themeColor;
			}
			@@ -491,8 +516,8 @@
			page && pageThemeColor && pageThemeColor[page]
			? pageThemeColor[page]
			: chapterNum && chapterThemeColor && chapterThemeColor[chapterNum]
			? chapterThemeColor[chapterNum]
			: bookThemeColor;
			? chapterThemeColor[chapterNum]
			: bookThemeColor;
			if (themeColor) {
			domItem.style.borderColor = themeColor;
			}
			@@ -554,17 +579,21 @@
			if (!this.questionDataMap[page]) {
			if (this.questionId && this.questionId[catalog]) {
			if (this.questionId[catalog][page]) {
			console.log(page,Array.isArray(this.questionId[catalog][page]));
			if(Array.isArray(this.questionId[catalog][page])) {
			this.questionDataMap[page] = await this.getQuestion(catalog, page,false);
			if (Array.isArray(this.questionId[catalog][page])) {
			this.questionDataMap[page] = await this.getQuestion(
			catalog,
			page,
			false
			);
			} else {
			const obj = {}
			const obj = {};
			for (let key in this.questionId[catalog][page]) {
			obj[key] = await this.getQuestion(catalog, page,key)
			obj[key] = await this.getQuestion(catalog, page, key);
			}
			this.questionDataMap[page] = obj
			this.questionDataMap[page] = obj;
			}
			}
			console.log(1, this.questionDataMap);
			}
			}
			// 渲染这一页的标记
			@@ -814,7 +843,7 @@
			// 记录高亮信息
			this.highlightData = data;
			// 跳转
			this.gotoPage(data.catalog, data.page, () => { });
			this.gotoPage(data.catalog, data.page, () => {});
			},
			// 获取题目列表
			getQuestionId() {
			@@ -826,7 +855,7 @@
			},
			// 获取题目收藏id列表
			getCollect() {
			if(!localStorage.getItem(this.config.tokenKey)) return false
			if (!localStorage.getItem(this.config.tokenKey)) return false;
			this.MG.identity
			.getUserKey({
			domain: "collectData",
			@@ -836,17 +865,20 @@
			try {
			const collect = JSON.parse(res[0].value);
			if (collect.length) {
			this.collectId = collect.find(item => item.type == 'json').collectList
			this.collectId = collect.find(
			(item) => item.type == "json"
			).collectList;
			}
			} catch (error) {
			console.log("暂无数据");
			}
			}).catch(res => {
			console.log('index 请求题目收藏id报错');
			})
			.catch((res) => {
			console.log("index 请求题目收藏id报错");
			});
			},
			// 获取章节题目
			async getQuestion(num, page,questionIndex) {
			async getQuestion(num, page, questionIndex) {
			let cardList = [
			{
			catalogName: "单选题",
			@@ -871,40 +903,57 @@
			];
			if (this.questionId) {
			if (this.questionId[num] && this.questionId[num][page]) {
			const res = await axios.get(
			this.config.activeBook.resourceUrl + "/question-" + num + ".json"
			);
			if (!res.data) return [];
			let ids = []
			questionIndex ? ids = this.questionId[num][page][questionIndex] : ids = this.questionId[num][page]
			for (let index = 0; index < res.data.data.length; index++) {
			const item = res.data.data[index];
			if (num != this.questionDataIndex) {
			// 判断当前章节的题目json是否已经请求过
			const res = await axios.get(
			this.config.activeBook.resourceUrl + "/question-" + num + ".json"
			);
			if (!res.data) return [];
			this.questionList = res.data.data;
			this.questionDataIndex = res.data.chapterNum;
			console.log("章节号", num, res);
			}
			let ids = [];
			questionIndex
			? (ids = this.questionId[num][page][questionIndex])
			: (ids = this.questionId[num][page]);
			for (let index = 0; index < this.questionList.length; index++) {
			const item = this.questionList[index];
			// 数学公式加类名去修改样式
			if (item.type && item.type == 'material') {
			if (!item.infoList.length) return false
			item.infoList.forEach(citem => {
			if (citem.answer) citem.answer = citem.answer.replace(/\<math/gi, '<math class="examination-math"')
			})
			if (item.type && item.type == "material") {
			if (!item.infoList.length) return false;
			item.infoList.forEach((citem) => {
			if (citem.answer)
			citem.answer = citem.answer.replace(
			/\<math/gi,
			'<math class="examination-math"'
			);
			});
			} else {
			if (item.answer) item.answer = item.answer.replace(/\<math/gi, '<math class="examination-math"')
			if (item.answer)
			item.answer = item.answer.replace(
			/\<math/gi,
			'<math class="examination-math"'
			);
			}
			item.isCollect = this.collectId.indexOf(item.id) > -1 ? true : false
			item.isCollect =
			this.collectId.indexOf(item.id) > -1 ? true : false;
			if (ids.indexOf(item.id) > -1) {
			if (item.type && item.type == "material") {
			cardList.push(item);
			} else {
			if (item.questionType == "judge") {
			cardList[1].infoList.push(item);
			}
			}
			if (item.questionType == "singleChoice") {
			cardList[0].infoList.push(item);
			}
			if (item.questionType == "multipleChoice") {
			}
			if (item.questionType == "multipleChoice") {
			cardList[2].infoList.push(item);
			}
			if (item.questionType == "completion") {
			}
			if (item.questionType == "completion") {
			cardList[3].infoList.push(item);
			}
			}
			if (item.questionType == "shortAnswer") {
			cardList[4].infoList.push(item);
			}
			@@ -917,17 +966,14 @@
			return [];
			}
			},

			// 视频小窗
			handleVideoPicture() {
			let doms = (
			this.container ? this.container : document
			).querySelectorAll(".video");
			doms = Array.from(doms)
			if (!doms.length) return false
			const playVudio = doms
			.reverse()
			.find((item) => item.paused == false);
			let doms = (this.container ? this.container : document).querySelectorAll(
			".video"
			);
			doms = Array.from(doms);
			if (!doms.length) return false;
			const playVudio = doms.reverse().find((item) => item.paused == false);
			if (playVudio) {
			const bottomGap = playVudio.getBoundingClientRect().bottom;
			const topGap = playVudio.getBoundingClientRect().top;
			@@ -935,7 +981,7 @@
			playVudio.requestPictureInPicture();
			}
			}
			}
			},
			},
			components: {
			pageHeader,

New file
			@@ -0,0 +1,58 @@
			<template>
			<div ref="ggbContainer" class="ggb-container"></div>
			</template>

			<script lang="ts">

			export default {
			mounted() {
			if (!window.GGBApplet) {
			const script = document.createElement("script");
			script.src = "https://www.geogebra.org/apps/deployggb.js";
			script.onload = () => {
			this.initGeoGebra();
			};
			document.body.appendChild(script);
			} else {
			this.initGeoGebra();
			}
			},
			methods:{
			initGeoGebra() {
			var params = {
			id: "ggbApplet",
			appName: "scientific",
			width: 600,
			height: 600,
			showToolBar: true,
			borderColor: null,
			showMenuBar: true,
			allowStyleBar: true,
			showAlgebraInput: true,
			enableLabelDrags: false,
			enableShiftDragZoom: true,
			capturingThreshold: null,
			showToolBarHelp: false,
			errorDialogsActive: true,
			showTutorialLink: true,
			showLogging: true,
			useBrowserForJS: false,
			};

			if (this.$refs.ggbContainer) {
			const applet = new GGBApplet(params, true);
			applet.inject(this.$refs.ggbContainer);
			}
			}
			}
			}

			</script>

			<style scoped>
			.ggb-container {
			width: 100%;
			height: 100%;
			/* 其他样式 */
			}
			</style>

			@@ -38,7 +38,7 @@
			<p
			class="titleText text-fl"
			v-if="
			value.stemStyle == 'Txt' && value.questionType != 'completion'
			value.stemStyle == 'Txt' && value.questionType != 'completion' && value.questionType !='dropdown'
			"
			:id="value.id"
			v-html="value.stem.stemTxt"
			@@ -73,6 +73,7 @@
			<span
			v-if="typeof itemText == 'string'"
			v-html="itemText"
			class="input-txt"
			></span>
			<input
			v-else
			@@ -91,6 +92,33 @@
			v-html="value.stem.stemTxt"
			v-cloak
			></p>
			<!-- 下拉选择题 -->
			<p class="titleText" v-if="value.questionType == 'dropdown'">
			<span
			v-for="(itemText, indexText) in value.stem"
			:key="indexText + 'questionType'"
			>
			<span
			v-if="typeof itemText == 'string'"
			v-html="itemText"
			class="input-txt"
			></span>
			<el-select
			v-else
			v-model="value.userAnswer"
			:disabled="value.isComplete"
			>
			<el-option
			v-for="citem in value.option"
			:key="citem.index"
			:label="citem.txt"
			:value="citem.value"
			>

			</el-option>
			</el-select>
			</span>
			</p>
			</div>
			<img
			:src="value.isCollect ? isHeart : heart"
			@@ -551,7 +579,6 @@
			watch: {
			cardList: {
			handler(newVal) {
			// console.log('新值',newVal);
			this.cardData = this.cardList;
			if (newVal && newVal.length) {
			this.loading = false;
			@@ -566,6 +593,18 @@
			this.getErrorList();
			},
			methods: {
			// 获取不受保护的图片
			getPublicImage(md5, width, height) {
			if(!md5) return
			if(md5.includes('http')) return md5
			let src = null;
			if (md5) {
			src = process.env.VUE_APP_API_URL + `/file/GetPreViewImage?md5=${md5}`;
			}
			if (width) src += `&width=${width}`;
			if (height) src += `&height=${height}`;
			return src;
			},
			// 数组转为字符串方法
			arrayToString(data) {
			// 检查是否为数组
			@@ -646,9 +685,9 @@
			}
			} else if (
			citem.questionType == "singleChoice" \|\|
			citem.questionType == "judge"
			citem.questionType == "judge" \|\|
			citem.questionType == 'dropdown'
			) {
			if (citem.id == "63825") console.log("i", item);
			citem.isRight = citem.answer == citem.userAnswer;
			} else if (citem.questionType == "shortAnswer") {
			// 简答翻译
			@@ -858,6 +897,12 @@
			</script>


			<style lang="less" >
			.titleText img {
			max-width: 80%;
			}
			</style>

			<style lang="less" scoped>
			.catalogName {
			text-indent: 1em !important;
			@@ -1010,11 +1055,14 @@
			font-size: 16px;
			line-height: 32px;
			color: #000;

			.input-txt {
			display: flex;
			flex-wrap: wrap;
			align-items: center;
			}
			span {
			display: inline-block;
			font-size: 16px;
			// line-height: 26px;
			color: #000;
			font-weight: 400;
			margin-top: 6px;