数学

闫增涛

2024-10-16 d7bb63ff28f0f08f377239139893fa5b263c844f

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

@@ -143,6 +143,15 @@
            <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>
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          <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>
@@ -152,7 +161,7 @@
          <p>其中<i>a</i>是自变量，定义域为{<i>a</i>|<i>a</i>＞0}.</p>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
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          <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>
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    <div class="page-box" page="81">
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        <ul class="page-header-odd fl al-end">
          <li>074</li>
          <li>074-076</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <h3 id="c026">习题3.1<span class="fontsz2">＞＞＞</span></h3>
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    <!-- 075 -->
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        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>075</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <div class="bj">
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0086-1.jpg" /></p>
            <p class="img">第2（2） 题图</p>
            <p>3.解答题.</p>
            <p>（1） 小梁第一季度和第二季度每月手机费充值如表3-3所示，请用函数的概念描述小梁每月手机费充值金额<i>y</i>（元）与月份<i>x</i>的对应关系.</p>
            <p class="img">表3-3</p>
            <p class="center"><img class="img-a" alt="" src="../../assets/images/0086-2.jpg" /></p>
            <p>（2） 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>
                  <mi>x</mi>
                  <mrow>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>1</mn>
                  </mrow>
                </mfrac>
              </math>；</p>
            <p>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>
                <mo>+</mo>
                <msqrt>
                  <mn>2</mn>
                  <mo>−</mo>
                  <mi>x</mi>
                </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>
                  <msup>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>−</mo>
                  <mn>5</mn>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>6</mn>
                </msqrt>
              </math>.</p>
            <p><span class="bj-sp"><b>水平二</b></span></p>
            <p>1.填空题.</p>
            <p>（1） 若函数<i>f</i>（<i>x</i>）=2<i>x</i>+<i>b</i>，且<i>f</i>（-1）=5，则<i>b</i>=____；</p>
            <p>（2） 若函数<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>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mn>2</mn>
                        <mo>−</mo>
                        <mi>x</mi>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≤</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <msup>
                          <mi>x</mi>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                        <mo>−</mo>
                        <mn>3</mn>
                        <mo>，</mo>
                        <mi>x</mi>
                        <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>，则<i>f</i>（-1）=____，<i>f</i>（<i>f</i>（-1））=</p>
            <p>____；</p>
            <p>（3） 若函数<i>f</i>（<i>t</i>-1）=4<i>t</i>+7，则<i>f</i>（2）=____.</p>
            <p>2.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>
                <msqrt>
                  <msup>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>−</mo>
                  <mn>16</mn>
                </msqrt>
              </math>；</p>
            <p>（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>
                <mfrac>
                  <mn>1</mn>
                  <msqrt>
                    <msup>
                      <mi>x</mi>
                      <mrow>
                        <mn>2</mn>
                      </mrow>
                    </msup>
                    <mo>−</mo>
                    <mn>3</mn>
                    <mi>x</mi>
                  </msqrt>
                </mfrac>
              </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>5</mn>
                  <mo>−</mo>
                  <mrow>
                    <mo stretchy="false">|</mo>
                  </mrow>
                  <mn>3</mn>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>1</mn>
                  <mo stretchy="false">|</mo>
                </msqrt>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mrow>
                    <mi>x</mi>
                    <mo>−</mo>
                    <mn>2</mn>
                  </mrow>
                </mfrac>
              </math>.</p>
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    <!-- 076 -->
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      <div v-if="showPageList.indexOf(83) > -1">
        <ul class="page-header-odd fl al-end">
          <li>076</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>

        <div class="padding-116">
          <div class="bj">
            <p>3.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>
                <msqrt>
                  <msup>
                    <mi>x</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msup>
                  <mo>−</mo>
                  <mn>4</mn>
                  <mi>x</mi>
                  <mo>+</mo>
                  <mn>3</mn>
                </msqrt>
              </math>.</p>
            <p>（1） 求函数的定义域；</p>
            <p>（2） 比较<i>f</i>（5）与<i>f</i>（3）的大小；</p>
            <p>（3） 求函数的值域.</p>
          </div>
          <h2 id="b016">3.2 函数的表示方法<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
          <h3 id="c027">3.2.1 函数的表示方法<span class="fontsz2">＞＞＞</span></h3>
@@ -684,6 +446,12 @@
          <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>
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            <p class="block">分组探讨，例2中的函数能否用解析法表示？例3中的函数能否用列表法和解析法表示？比较函数的三种表示方法，它们各自的特点是什么？</p>
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              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
            </div>
            <p class="block">依法纳税是每个公民的义务.查找国家征收个人所得税税率表， 并讨论：如果一个公司内两位员工一年的个人综合所得额分别为12万和15万，那么这两位员工所缴纳的个人所得税税额分别是多少？
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          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <p>1.填空题.</p>
            <p>（1） 若函数<math display="0">
                <mi>y</mi>
                <mo>=</mo>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mi>x</mi>
                        <mo>+</mo>
                        <mn>1</mn>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>∈</mo>
                        <mrow data-mjx-texclass="INNER">
                          <mo data-mjx-texclass="OPEN">{</mo>
                          <mn>0</mn>
                          <mo>，</mo>
                          <mn>1</mn>
                          <mo>，</mo>
                          <mn>2</mn>
                          <mo data-mjx-texclass="CLOSE">}</mo>
                        </mrow>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>2</mn>
                        <mi>x</mi>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>∈</mo>
                        <mrow data-mjx-texclass="INNER">
                          <mo data-mjx-texclass="OPEN">{</mo>
                          <mn>3</mn>
                          <mo>，</mo>
                          <mn>4</mn>
                          <mo data-mjx-texclass="CLOSE">}</mo>
                        </mrow>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>，则<i>f</i>（0）=____，<i>f</i>（3）=____；</p>
            <p>（2） 若函数<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>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mn>3</mn>
                        <mi>x</mi>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>＜</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <msqrt>
                          <mi>x</mi>
                        </msqrt>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≥</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>____，</p>
            <p><i>f</i>（4）=____；</p>
            <p>（3） 若函数<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>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mn>3</mn>
                        <mi>x</mi>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≤</mo>
                        <mo>−</mo>
                        <mn>2</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>2020</mn>
                        <mo>，</mo>
                        <mo>−</mo>
                        <mn>2</mn>
                        <mo>＜</mo>
                        <mi>x</mi>
                        <mo>≤</mo>
                        <mn>2</mn>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <msup>
                          <mi>x</mi>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>＞</mo>
                        <mn>2</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>，则<i>f</i>（-1）=____，<i>f</i>（0）=____，<i>f</i>（3）=____；</p>
            <p>（4） 若函数<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>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <msup>
                          <mi>x</mi>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                        <mo>+</mo>
                        <mn>3</mn>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>＜</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <msqrt>
                          <mn>2</mn>
                          <mi>x</mi>
                          <mo>+</mo>
                          <mn>1</mn>
                        </msqrt>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≥</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>____.</p>
            <p>2.为了促销某品牌的薯片，某电商平台拟采取如下促销方式：每袋薯片原来的价格是6元，若顾客购买30袋及以上，则每袋的价格为5元.假设某顾客一次性购买这种薯片<i>x</i>袋，电商平台收款是<i>y</i>元.
            </p>
            <p>（1） 当<i>x</i>＜30，<i>x</i>∈<b>N</b>时，写出<i>y</i>与<i>x</i>的函数关系式；</p>
            <examinations :cardList="questionData[88] ? questionData[88][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
            v-if="questionData" ></examinations>
          </div>
        </div>
      </div>
@@ -1309,205 +858,15 @@
    <div class="page-box" page="89">
      <div v-if="showPageList.indexOf(89) > -1">
        <ul class="page-header-odd fl al-end">
          <li>082</li>
          <li>082-084</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>

        <div class="padding-116">
          <div class="bj">
            <p>（2） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.</p>
            <p>3.某市居民家庭燃气收费采用分段计费方式，如表3-8所示.</p>
            <p>（1） 小黄家8月使用燃气46 m<sup>3</sup>，他家应付燃气费多少元；</p>
            <p>（2） 用解析法表示每户居民家庭每月缴纳燃气费<i>y</i>（元）与使用燃气量<i>x</i>（<i>m</i><sup>3</sup>）的函数关系，并画出函数的图像.</p>
            <p class="img">表3-8 某市居民家庭每月用燃气计费价格表</p>
            <p class="center"><img class="img-a" alt="" src="../../assets/images/0093-1.jpg" /></p>
          </div>
          <h3 id="c029">习题3.2<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <p><span class="bj-sp"><b>水平一</b></span></p>
            <p>1.选择题.</p>
            <p>（1） 某商场有某品牌的电动车30辆可供出售，每辆售价2 000元，那么该商场出售电动车的营业额<i>y</i>（元）与出售的数量<i>x</i>之间的函数关系用解析法表示正确的是（　）.</p>
            <p>A.<i>y</i>=2 000<i>x</i></p>
            <p>B.<i>y</i>=2 000<i>x</i>，<i>x</i>≤30</p>
            <p>C.<i>y</i>=2 000<i>x</i>，<i>x</i>≤30，且<i>x</i>∈<b>N</b></p>
            <p>D.<i>y</i>=30<i>x</i></p>
            <p>（2） 若函数<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>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <msup>
                          <mi>x</mi>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≤</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>2</mn>
                        <mi>x</mi>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>＞</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>，则<i>f</i>（-1）+<i>f</i>（1）=（　）.</p>
            <p>A.0</p>
            <p>B.2</p>
            <p>C.3</p>
            <p>D.4</p>
            <p>2.市场上新上市的苹果价格是7.2元/kg，用解析法表示购买苹果应付款<i>y</i>（元）与购买质量<i>x</i>（kg ）的函数关系.</p>
            <p>3.某快递公司在<i>A</i>城内的运费价格如表3-9所示，用<i>x</i>（kg ）表示物品的质量，<i>y</i>（元）表示快递物品的运费.</p>
          </div>
        </div>
      </div>
    </div>
    <!-- 083 -->
    <div class="page-box" page="90">
      <div v-if="showPageList.indexOf(90) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>083</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <div class="bj">
            <p class="img">表3-9</p>
            <p class="center"><img class="img-a" alt="" src="../../assets/images/0094-1.jpg" /></p>
            <p>（1） 某顾客在<i>A</i>城内快递物品，如果质量是2.5 kg，那么他应付快递费多少元？</p>
            <p>（2） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）.</p>
            <p>（3） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像.</p>
            <p>4.某城市公交车2号线路共设置10站，乘车收费标准为：乘客若乘坐不超过6站则收费2元；若乘坐超过6 站则收费4元.用<i>x</i>表示乘车的站数，<i>y</i>表示收费金额.</p>
            <p>（1） 用列表法表示公交车收费<i>y</i>与乘车的站数<i>x</i>之间的函数关系；</p>
            <p>（2） 用解析法表示函数<i>y</i>=<i>f</i>（<i>x</i>）；</p>
            <p>（3） 画出函数<i>y</i>=<i>f</i>（<i>x</i>）的图像.</p>
            <p>5.某商户以每千克30元的价格购入100 kg
              某种野生菌，并把野生菌放入冷库中，但最多只能存放15天.据预测，这批野生菌的单价每天将上涨0.2元.在不考虑其他因素的情况下，这批野生菌的售价<i>y</i>（元）是存放天数<i>x</i>的函数.</p>
            <p>（1） 写出函数的定义域；</p>
            <p>（2） 用解析法表示<i>y</i>与<i>x</i>的函数关系；</p>
            <p>（3） 设一次性出售这批野生菌可获利<i>P</i>元，用解析法表示<i>P</i>与<i>x</i>的函数关系.</p>
            <p><span class="bj-sp"><b>水平二</b></span></p>
            <p>1.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>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mi>x</mi>
                        <mo>+</mo>
                        <mn>2</mn>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≤</mo>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <msup>
                          <mi>x</mi>
                          <mrow>
                            <mn>2</mn>
                          </mrow>
                        </msup>
                        <mo>，</mo>
                        <mo>−</mo>
                        <mn>1</mn>
                        <mo>＜</mo>
                        <mi>x</mi>
                        <mo>＜</mo>
                        <mn>2</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>3</mn>
                        <mi>x</mi>
                        <mo>，</mo>
                        <mi>x</mi>
                        <mo>≥</mo>
                        <mn>2.</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>
            <p>（1） 求<i>f</i>（0）+<i>f</i>（4）的值；</p>
            <p>（2） 若<i>f</i>（<i>x</i>）=3，求<i>x</i>的值.</p>
            <p>2.某市出租车的计价标准：按出租车实际行驶路程计费，4 km及以下收费10元，超过4 km的部分按2元/km计费.</p>
          </div>
        </div>
      </div>
    </div>
    <!-- 084 -->
    <div class="page-box" page="91">
      <div v-if="showPageList.indexOf(91) > -1">
        <ul class="page-header-odd fl al-end">
          <li>084</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">
          <div class="bj">
            <p>（1） 如果某人搭乘出租车行驶了20 km，那么他需要付费多少元？</p>
            <p>（2） 请表示出租车收费<i>y</i>（元）与行驶的路程<i>x</i>（km） 之间的函数关系；</p>
            <p>（3） 画出（2） 中函数的图像.</p>
            <p>3.为鼓励居民节约用水，某自来水公司按表3-10的收费标准收取每户居民家庭每月水费.</p>
            <p class="img">表3-10</p>
            <p class="center"><img class="img-a" alt="" src="../../assets/images/0095-1.jpg" /></p>
            <p>（1） 小明家8月的用水量是13 <i>t</i>，小王家8月的用水量是16 <i>t</i>，小明家和小王家分别应付水费多少元？</p>
            <p>（2） 写出每户家庭居民每月付水费<i>y</i>（元）与用水量<i>x</i>（<i>t</i>）的函数关系，并画出该函数的图像；</p>
            <p>（3） 若小李家9月付水费66元，则他家这个月的用水量是多少？</p>
            <examinations :cardList="questionData[89]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
            v-if="questionData" ></examinations>
          </div>
          <h2 id="b017">3.3 函数的单调性和奇偶性<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
          <h3 id="c030">3.3.1 函数的单调性<span class="fontsz2">＞＞＞</span></h3>
@@ -1517,6 +876,12 @@
          </p>
        </div>
      </div>
    </div>
    <!-- 083 -->
    <div class="page-box hidePage" page="90">
    </div>
    <!-- 084 -->
    <div class="page-box hidePage" page="91">
    </div>
    <!-- 085 -->
    <div class="page-box" page="92">
@@ -2350,6 +1715,15 @@
            <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">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[103] ? questionData[103][1] : []" :hideCollect="true" sourceType="json" v-if="questionData">
            </examinations>
          </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">
@@ -2483,7 +1857,7 @@
            <div class="bj1-hzjl">
              <p class="left"><img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" /></p>
            </div>
            <examinations :cardList="questionData[103]" :hideCollect="true" sourceType="json"
            <examinations :cardList="questionData[103] ? questionData[103][2] : []" :hideCollect="true" sourceType="json"
            v-if="questionData" ></examinations>
          </div>
        </div>
@@ -2714,7 +2088,7 @@
    <div class="page-box" page="109">
      <div v-if="showPageList.indexOf(109) > -1">
        <ul class="page-header-odd fl al-end">
          <li>102</li>
          <li>102-103</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
@@ -2793,21 +2167,6 @@
          <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>
    <!-- 103 -->
    <div class="page-box" page="110">
      <div v-if="showPageList.indexOf(110) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>103</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <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"
@@ -2815,6 +2174,9 @@
          </div>
        </div>
      </div>
    </div>
    <!-- 103 -->
    <div class="page-box hidePage" page="110">
    </div>
    <!-- 104 -->
    <div class="page-box" page="111">
@@ -3238,7 +2600,6 @@
    },
    showNext(num) {
      const number = this.thinkOne.findIndex((item, index) => index == num);
      console.log(number);
      this.thinkOne[number].isShow = true;
      if (this.thinkIndex <= 2) {
        this.thinkIndex++;