testbookLayout.git

			@@ -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>
			@@ -149,19 +173,32 @@
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[78] ? questionData[78][1] : []" :hideCollect="true" sourceType="json" v-if="questionData">
			<examinations :cardList="questionData[78] ? questionData[78][1] : []" sourceType="json" v-if="questionData">
			</examinations>
			</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"
			<examinations :cardList="questionData[78] ? questionData[78][2] : []" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -176,10 +213,6 @@
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<div class="bj">
			<p>（3）若函数<i>f</i>（<i>x</i>）=2<i>x</i>-1，则<i>f</i>（<i>t</i>）=___，<i>f</i>（<i>f</i>（5））=____.</p>
			<p>2.一列动车从A城以每小时200km的速度匀速直线行驶4 h后到达B城.该动车在行驶过程中，行驶的路程是时间的函数吗？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.</p>
			</div>
			<p>从上面的学习可以知道，一个函数包含定义域、对应关系和值域.函数的值域是由函数的定义域和对应关系决定的.</p>
			<p>通常函数的定义域隐含在函数关系中.例如，我们不能计算当<i>x</i>=0时<math display="0">
			<mi>f</mi>
			@@ -195,42 +228,54 @@
			</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>
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			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
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			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">
			@@ -257,159 +302,214 @@
			<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"
			<examinations :cardList="questionData[80]" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -426,7 +526,7 @@
			<div class="padding-116">
			<h3 id="c026">习题3.1<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj" >
			<examinations :cardList="questionData[81]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[81]" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			<h2 id="b016">3.2 函数的表示方法<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
			@@ -435,15 +535,39 @@
			<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 +589,88 @@
			</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>
			@@ -507,20 +683,16 @@
			<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>
			</div>
			<examinations :cardList="questionData[85] ? questionData[85][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[85] ? questionData[85][1] : []" 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[85] ? questionData[85][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[85] ? questionData[85][2] : []" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -712,7 +884,22 @@
			<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 +912,20 @@
			<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 +934,130 @@
			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>
			@@ -832,23 +1073,17 @@
			</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>
			</div>
			<examinations :cardList="questionData[88] ? questionData[88][1] : []" :hideCollect="true" sourceType="json"
			<examinations :cardList="questionData[88] ? questionData[88][1] : []" sourceType="json"
			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[88] ? questionData[88][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[88] ? questionData[88][2] : []" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -865,7 +1100,7 @@
			<div class="padding-116">
			<h3 id="c029">习题3.2<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[89]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[89]" 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>
			@@ -947,12 +1182,32 @@
			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 +1229,21 @@
			<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 +1251,9 @@
			<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 +1262,7 @@
			<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 +1281,158 @@
			<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>
			@@ -1147,7 +1447,7 @@
			<div class="padding-116">
			<p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
			<div class="bj">
			<examinations :cardList="questionData[95]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[95]" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -1236,23 +1536,17 @@
			</p>
			<p class="img fl fl-cn ju-cn">
			<span>图3-15</span>
			<el-tooltip class="item" effect="dark" :content="chapterData.isCollectImg ? '点击取消' : '点击收藏'"
			placement="top-start">
			<img :src="collectResourceList.findIndex(item => item.id == '722FE833') > -1 ? collectCheck : collectImg"
			alt="" class="collect-btn" @click="handleCollect('img')" />
			</el-tooltip>
			</p>
			<video :src="videoPath" webkit-playsinline="true" x-webkit-airplay="true" playsinline="true"
			x5-video-orientation="h5" x5-video-player-fullscreen="true" x5-playsinline="" controls
			controlslist="nodownload" class="video-border w100"></video>
			<p class="img fl fl-cn ju-cn">
			<span>视频：判数函数奇偶性的方法和步骤 </span>
			<el-tooltip class="item" effect="dark" :content="chapterData.isCollectVideo ? '点击取消' : '点击收藏'"
			placement="top-start">
			<img
			:src="collectResourceList.findIndex(item => item.id == 'a28cd862d61b5df2201406b76e9f01b0') > -1 ? collectCheck : collectImg"
			alt="" class="collect-btn" @click="handleCollect('video')" />
			</el-tooltip>
			</p>
			<p class="fl">
			<span>
			@@ -1310,17 +1604,20 @@
			<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 +1641,11 @@
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			<span class="btn-box" @click="openThinkingDialog">
			<span class="btn-box" @click="openDialog(thinkOne)">
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			transform="translate(-3316.14 15289.201)" />
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			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">
			@@ -1475,7 +1759,7 @@
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[98]" :hideCollect="true" sourceType="json"
			<examinations :cardList="questionData[98]" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -1492,18 +1776,24 @@
			<div class="padding-116">
			<p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
			<div class="bj" >
			<examinations :cardList="questionData[99]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[99]" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			<p class="gr-title">
			四、函数 f(x)=x’-3 的图像在
			轴左边的部分如图所示，请你画出这个函数图像在 y轴右边的部分.
			</p>
			<div>
			<paint
			<!-- <paint
			:page="99"
			:imgUrl="
			this.config.activeBook.resourceUrl + '/images/0103-2.jpg'
			"
			/> -->
			<graffiti
			:page="99"
			:bcImg="this.config.activeBook.resourceUrl + '/images/0103-2.jpg'"
			:imgWidth="520"
			:imgHeight="494"
			/>
			</div>
			</div>
			@@ -1561,10 +1851,21 @@
			<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 +1882,111 @@
			</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 +1995,68 @@
			<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>
			@@ -1711,153 +2069,204 @@
			<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">
			<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 :cardList="questionData[103] ? questionData[103][1] : []" 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">
			<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>
			</div>
			<examinations :cardList="questionData[103] ? questionData[103][2] : []" :hideCollect="true" sourceType="json"
			<examinations :cardList="questionData[103] ? questionData[103][2] : []" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -1877,7 +2286,7 @@
			<div class="padding-116">
			<p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
			<div class="bj">
			<examinations :cardList="questionData[104]" :hideCollect="true" sourceType="json"
			<examinations :cardList="questionData[104]" sourceType="json"
			v-if="questionData" ></examinations>
			</div>

			@@ -1901,7 +2310,7 @@
			<div class="padding-116">
			<h3 id="c032">习题3.3<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj" >
			<examinations :cardList="questionData[105]" :hideCollect="true" sourceType="json"
			<examinations :cardList="questionData[105]" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			<h2 id="b018">3.4 函数的应用<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
			@@ -1921,101 +2330,147 @@
			<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><</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><</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><</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><</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><</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><</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 +2486,192 @@
			</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>
			@@ -2093,83 +2684,9 @@
			<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"
			<examinations :cardList="questionData[110]" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -2189,7 +2706,7 @@
			<div class="padding-116">
			<h3 id="c033">习题3.4<span class="fontsz2">＞＞＞</span></h3>
			<div class="bj">
			<examinations :cardList="questionData[111]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			<examinations :cardList="questionData[111]" sourceType="json" inputBc="#d3edfa"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -2296,7 +2813,7 @@
			<div class="padding-116">
			<h2 id="b021">单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
			<div class="bj" >
			<examinations :cardList="questionData[117]" :hideCollect="true" sourceType="json"
			<examinations :cardList="questionData[117]" sourceType="json"
			v-if="questionData" ></examinations>
			</div>
			</div>
			@@ -2308,7 +2825,7 @@
			<!-- 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 +2842,11 @@
			<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 +2859,8 @@
			</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 +2868,17 @@
			<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
			@@ -2426,9 +2895,18 @@

			<script>
			import paint from '@/components/paint/index.vue'
			import graffiti from '@/components/graffiti/index.vue'
			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: {
			@@ -2440,9 +2918,10 @@
			type: Object,
			},
			},
			components: {examinations,paint},
			components: {examinations,paint,graffiti},
			data() {
			return {
			...showObj,
			collectImg: require("../../assets/images/icon/heart.png"),
			collectCheck: require("../../assets/images/icon/heart-check.png"),
			isShowExampleOne: false,
			@@ -2452,7 +2931,6 @@
			isShowExampleFive: false,
			dialogVisible: false,
			thinkingDialog: false,
			stepDialog: false,
			videoPath: "",
			stepIndex: 1,
			thinkIndex: 1,
			@@ -2463,103 +2941,32 @@
			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.'
			]
			};
			},
			@@ -2592,29 +2999,21 @@
			}
			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) {
			console.log(this.collectResourceList);
			let list = this.collectResourceList
			if (list.findIndex(item => item.id == id) > -1) {
			list = list.filter(item => item.id != id)
			@@ -2636,14 +3035,6 @@
			</script>

			<style lang="less" scoped>

			.iframe-box {
			width: 100%;
			min-height: 800px;
			border: 1px solid #00a1e9;
			border-radius: 10px;
			}

			li {
			list-style: none;
			}