闫增涛
2025-01-24 9f0a7ae776a4004d094d3d0d9b2170c0d9b448de
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          <img class="img-0" alt="" src="../../assets/images/dy3.jpg" />
        </h1>
        <div class="padding-116">
          <p>
            在客观世界中存在各种各样的运动变化现象.如搭载神舟十四号载人飞船的长征二号运载火箭发射过程中,飞船与发射点距离会随着时间的变化而变化;深海勇士号载人潜水器在下潜实验过程中,其压强随着下潜深度的增加而增大;代表新能源技术的光伏发电和风能发电,我国的装机容量随时间变化而增长;我国快速发展的高速铁路,其总里程是逐年增加的,现已突破4万km
            ,稳居世界第一;每个人的体温随着时间的变化而变化;到商店购买同一种饮料的数量越多,付费越多等.这些动态变化现象都表现为变量之间的对应关系,我们常用函数模型来描述这些变量之间的关系和规律,并通过研究函数来认识客观世界.
          </p>
          <p>
            函数是描述客观世界变化规律和解决数学问题的重要工具.它与代数式、方程、不等式等知识联系紧密,是进一步学习数学的重要基础.函数的概念及其反映的数学思想和方法已广泛渗透到数学的各个领域,并在现实生活中有着广泛的应用.
          </p>
          <p>
            本单元主要学习函数的概念、函数的表示方法、函数的单调性和奇偶性以及函数的应用.本单元的学习,重在感受用直观想象从具体问题中抽象出数学问题,并用精确的数学符号语言表达概念、性质、推理等;掌握研究函数的基本内容、过程和方法;运用建立分段函数、二次函数等数学模型解决实际问题的方法;积累一定的数学经验和方法,提升直观想象、数学抽象、数学建模、逻辑推理等核心素养.
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            <p>1.函数的概念.</p>
            <p>
              能从具体情境中抽象概括出函数的概念,学习用集合语言和对应关系描述函数概念.
            </p>
            <p>2.函数的表示方法.</p>
            <p>了解函数的三种表示方法,会恰当地选用这些方法表示函数;</p>
            <p>理解分段函数的概念;</p>
            <p>通过研究函数的变化规律来把握客观世界中事物的变化规律.</p>
            <p>3.函数的单调性和奇偶性.</p>
            <p>
              学习用精准的数学符号语言描述函数的性质,掌握判断函数单调性和奇偶性的方法.
            </p>
            <p>4.函数的应用.</p>
            <p>初步掌握建立分段函数、二次函数模型来解决实际问题的方法;</p>
            <p>能运用函数的思想和方法解决实际问题,提升核心素养和思维品质.</p>
          </div>
        </div>
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      <div v-if="showPageList.indexOf(6) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>089</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <h3 id="c031">
            3.3.2 函数的奇偶性<span class="fontsz2">>>></span>
          </h3>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
          </p>
          <p>
            函数<i>f</i>(<i>x</i>)=|<i>x</i>|和<i>g</i>(<i>x</i>)=<i>x</i
            ><sup>2</sup>的图像的对称性如何?
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          <p>
            列出表3-11和表3-12,画出函数<i>f</i>(<i>x</i>)=|<i>x</i>|
            和<i>g</i>(<i>x</i>)=<i>x</i><sup>2</sup>的图像,如图3-14(1)
            和(2) 所示.
          </p>
          <p class="img">表3-11</p>
          <p class="center">
            <img class="img-a" alt="" src="../../assets/images/0100-1.jpg" />
          </p>
          <p class="img">表3-12</p>
          <p class="center">
            <img class="img-a" alt="" src="../../assets/images/0100-2.jpg" />
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            <img class="img-c" alt="" src="../../assets/images/0100-3.jpg" />
          </p>
          <p class="img">图3-14</p>
          <p>
            观察图3-14(1)
            发现,函数<i>f</i>(<i>x</i>)=|<i>x</i>|的定义域是(-∞,+∞),函数图像关于<i>y</i>轴对称.从表3-11中还发现,当自变量取一对相反数时,对应的函数值相等,如<i>f</i>(-1)=<i>f</i>(1)=1,<i>f</i>(-2)=<i>f</i>(2)=2,<i>f</i>(-3)=<i>f</i>(3)=3,…实际上,对任意<i>x</i>∈(-∞,+∞),都有<i>f</i>(-<i>x</i>)=|-<i>x</i>|=|<i>x</i>|=<i>f</i>(<i>x</i>),即<i>f</i>(-<i>x</i>)=<i>f</i>(<i>x</i>).
          </p>
          <p>
            图3-14(2) 中,函数<i>g</i>(<i>x</i>)=<i>x</i
            ><sup>2</sup
            >的定义域是(-∞,+∞),函数图像也关于<i>y</i>轴对称.表3-12中,当自变量取一对相反数时,对应的函数值相等,如<i>g</i>(-1)=<i>g</i>(1)=1,<i>g</i>(-2)=<i>g</i>(2)=4,<i>g</i>(-3)=<i>g</i>(3)=9,…实际上,对任意<i>x</i>∈(-∞,+∞),都有<i>g</i>(-<i>x</i>)=(-<i>x</i>)<sup>2</sup>=<i
              >x</i
            ><sup>2</sup
            >=<i>g</i>(<i>x</i>),即<i>g</i>(-<i>x</i>)=<i>g</i>(<i>x</i>).
          </p>
          <p>
            这两个函数的图像都关于 <i>y</i> 轴对称;当自变量取定义域中任意一对相
          </p>
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      <div v-if="showPageList.indexOf(7) > -1">
        <ul class="page-header-odd fl al-end">
          <li>090</li>
          <li>数学.基础模块</li>
          <li></li>
        </ul>
        <div class="padding-116">
          <p class="t0">反数时,对应的函数值都相等,这种函数就是偶函数.</p>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
          </p>
          <p>
            一般地,设函数<i>f</i>(<i>x</i>)的定义域为<i>D</i>,如果对于<span
              class="u"
              >任意</span
            ><i>x</i>∈<i>D</i>,<span class="u">都有</span
            >-<i>x</i>∈<i>D</i>,且<i>f</i>(-<i>x</i>)=<i>f</i>(<i>x</i>),那么函数<i>f</i>(<i>x</i>)就叫作<b>偶函数</b>,如图3-15所示.<b>偶函数的图像关于<i>y</i>轴对称</b>.
          </p>
          <p>
            我们可以由函数的图像是否关于<i>y</i>轴对称来判断函数是不是偶函数.
          </p>
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            <img
              class="img-c"
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            <span>图3-15</span>
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            <span>视频:判数函数奇偶性的方法和步骤 </span>
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              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>
              <span class="zt-ls"><b>例1</b></span
              > 根据图3-16中函数的图像,判断哪些函数是偶函数.
            </span>
            <span class="btn-box" @click="isShowExampleOne = !isShowExampleOne">
              <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 openImgBox">
            <img class="img-c" alt="" src="../../assets/images/0101-2.jpg" />
          </p>
          <p class="img">图3-16</p>
          <div v-if="isShowExampleOne">
            <p>
              <span class="zt-ls"><b>解</b></span> 在四个函数图像中,图3-16(1)
              和图3-16(4) 的函数图像关于<i>y</i>轴对称;图3-16(2)
              和图3-16(3)
              的函数图像不关于<i>y</i>轴对称.根据偶函数的图像具有关于<i>y</i>轴对称的特点,图3-16(1)和图3-16(4)的函数是偶函数,图3-16(2)和图3-16(3)的函数不是偶函数.
            </p>
          </div>
        </div>
      </div>
    </div>
    <div class="page-box" page="8">
      <div v-if="showPageList.indexOf(8) > -1">
        <ul class="page-header-box">
          <li>
            <p>第三单元 函数</p>
          </li>
          <li>
            <p><span>091</span></p>
          </li>
        </ul>
        <div class="padding-116">
          <p class="fl">
            <span>
              <span class="zt-ls"><b>例2</b></span>
               已知<i>f</i>(<i>x</i>)=|<i>x</i>|+1图像在<i>y</i>轴右边的部分如图3-17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="isShowExampleTwo = !isShowExampleTwo">
              <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 openImgBox">
            <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>
          <div class="bk">
            <div class="bj1">
              <p class="left">
                <img
                  class="img-gn1"
                  alt=""
                  src="../../assets/images/tbts.jpg"
                />
              </p>
            </div>
            <p class="block">
              一个函数是不是偶函数,可以由函数的图像是否关于<i>y</i>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.
            </p>
          </div>
          <p>
            <span class="zt-ls"><b>例3</b></span
            > 判断下列函数是不是偶函数.
          </p>
          <ul>
            <li class="fl fl-cn">
              <p>(1) <i>f</i>(<i>x</i>)=3<i>x</i><sup>2</sup>+1;</p>
              <span
                class="btn-box"
                @click="isShowExampleThree = !isShowExampleThree"
              >
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                  xmlns="http://www.w3.org/2000/svg"
                  width="16.501"
                  height="16.501"
                  viewBox="0 0 20.501 20.501"
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                    class="a"
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              </span>
              <span class="btn-box" @click="openThinkingDialog">
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                      d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
                      transform="translate(398 948)"
                    />
                    <path
                      class="b"
                      d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
                      transform="translate(398 948)"
                    />
                    <path
                      class="a"
                      d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
                      transform="translate(398 948)"
                    />
                  </g>
                </svg>
              </span>
            </li>
            <li class="fl fl-cn">
              <p>(2) <i>f</i>(<i>x</i>)=<i>x</i><sup>2</sup>+<i>x</i>;</p>
              <span
                class="btn-box"
                @click="isShowExampleFour = !isShowExampleFour"
              >
                <svg
                  xmlns="http://www.w3.org/2000/svg"
                  width="16.501"
                  height="16.501"
                  viewBox="0 0 20.501 20.501"
                >
                  <path
                    class="a"
                    d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                    transform="translate(-3327.144 15329)"
                  />
                </svg>
              </span>
              <span class="btn-box" @click="openMathDiaolog">
                <svg
                  xmlns="http://www.w3.org/2000/svg"
                  xmlns:xlink="http://www.w3.org/1999/xlink"
                  width="15.323"
                  height="15.939"
                  viewBox="0 0 18.323 15.939"
                >
                  <g transform="translate(-398 -946)">
                    <path
                      class="a"
                      d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
                      transform="translate(398 948)"
                    />
                    <path
                      class="b"
                      d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
                      transform="translate(398 948)"
                    />
                    <path
                      class="a"
                      d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
                      transform="translate(398 948)"
                    />
                  </g>
                </svg>
              </span>
            </li>
            <li class="fl fl-cn">
              <p>(3) <i>f</i>(<i>x</i>)=5<i>x</i>+2.</p>
              <span
                class="btn-box"
                @click="isShowExampleFive = !isShowExampleFive"
              >
                <svg
                  xmlns="http://www.w3.org/2000/svg"
                  width="16.501"
                  height="16.501"
                  viewBox="0 0 20.501 20.501"
                >
                  <path
                    class="a"
                    d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                    transform="translate(-3327.144 15329)"
                  />
                </svg>
              </span>
              <span class="btn-box" @click="openMathDiaolog">
                <svg
                  xmlns="http://www.w3.org/2000/svg"
                  xmlns:xlink="http://www.w3.org/1999/xlink"
                  width="15.323"
                  height="15.939"
                  viewBox="0 0 18.323 15.939"
                >
                  <g transform="translate(-398 -946)">
                    <path
                      class="a"
                      d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
                      transform="translate(398 948)"
                    />
                    <path
                      class="b"
                      d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
                      transform="translate(398 948)"
                    />
                    <path
                      class="a"
                      d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
                      transform="translate(398 948)"
                    />
                  </g>
                </svg>
              </span>
            </li>
          </ul>
          <div v-if="isShowExampleThree">
            <p>
              <span class="zt-ls"><b>解</b></span
              >(1) 函数<i>f</i>(<i>x</i>)=3<i>x</i
              ><sup>2</sup
              >+1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>,
            </p>
            <p>而</p>
            <p class="center">
              <i>f</i>(-<i>x</i>)=3(-<i>x</i>)<sup>2</sup>+1=3<i>x</i
              ><sup>2</sup>+1=<i>f</i>(<i>x</i>),
            </p>
            <p>
              所以,函数<i>f</i>(<i>x</i>)=3<i>x</i><sup>2</sup>+1是偶函数.
            </p>
          </div>
          <div v-if="isShowExampleFour">
            <p>
              (2) 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>,而
            </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>≠<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>不是偶函数.
            </p>
          </div>
          <div v-if="isShowExampleFive">
            <p>
              (3)
              函数<i>f</i>(<i>x</i>)=5<i>x</i>+2的定义域是<b>R</b>,对任意<i>x</i>∈<b>R</b>,都有-<i>x</i>∈<i>R</i>,而
            </p>
            <p class="center">
              <i>f</i
              >(-<i>x</i>)=5(-<i>x</i>)+2=-5<i>x</i>+2≠<i>f</i>(<i>x</i>),
            </p>
            <p>所以,函数<i>f</i>(<i>x</i>)=5<i>x</i>+2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>
            <p class="block tl">
              如果<i>f</i>(<i>x</i>),<i>g</i>(<i>x</i>)都是定义域为<i>D</i>的偶函数,那么<i>f</i>(<i>x</i>)+<i>g</i>(<i>x</i>)和<i>f</i>(<i>x</i>)<i>g</i>(<i>x</i>)仍是偶函数吗?
              <textarea
                cols="30"
                rows="4"
                v-model="chapterData.txtTwo"
                placeholder="请输入内容"
                class="w100 ta-br textarea-text"
                @input="handleChapterData"
              ></textarea>
            </p>
          </div>
        </div>
      </div>
    </div>
    <div class="page-box" page="9">
      <div v-if="showPageList.indexOf(9) > -1">
        <ul class="page-header-odd fl al-end">
          <li>092</li>
          <li>数学.基础模块</li>
          <li></li>
        </ul>
        <div class="padding-116">
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
          <div class="bj">
            <examinations
              :cardList="questionData[9]"
              :hideCollect="true"
              sourceType="json"
              inputBc="#d3edfa"
              v-if="questionData"
              :isReal="false"
            ></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 style="margin: 0 auto; width: 330px">
              <graffiti
                :page="9"
                :bcImg="
                  this.config.activeBook.resourceUrl + '/images/0103-2.jpg'
                "
                :imgHeight="300"
                :imgWidth="300"
                :bcColor="'#d3edfa'"
              />
            </div>
          </div>
        </div>
      </div>
    </div>
    <!-- 函数控件弹窗 -->
    <el-dialog
      :visible.sync="dialogVisible"
      width="60%"
      :append-to-body="true"
      :show-close="false"
    >
      <div slot="title" style="padding: 0 0 15px 0; position: relative">
        <svg
          style="position: absolute; right: 10px; cursor: pointer"
          @click="dialogVisible = false"
          t="1718596022986"
          class="icon"
          viewBox="0 0 1024 1024"
          version="1.1"
          xmlns="http://www.w3.org/2000/svg"
          p-id="4252"
          width="20"
          height="20"
          xmlns:xlink="http://www.w3.org/1999/xlink"
        >
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797"
            p-id="4253"
          ></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797"
            p-id="4254"
          ></path>
        </svg>
      </div>
      <iframe
        src="https://www.geogebra.org/calculator"
        frameborder="0"
        style="width: 100%; min-height: 800px"
      ></iframe>
    </el-dialog>
    <!-- 解题思路弹窗 -->
    <el-dialog
      :visible.sync="thinkingDialog"
      width="40%"
      :append-to-body="true"
      :show-close="false"
    >
      <div
        slot="title"
        style="
          padding: 0;
          text-align: center;
          color: #333;
          display: flex;
          justify-content: center;
        "
      >
        <span style=""> 解题思路 </span>
        <svg
          style="position: absolute; right: 10px; cursor: pointer"
          @click="thinkingDialog = false"
          t="1718596022986"
          class="icon"
          viewBox="0 0 1024 1024"
          version="1.1"
          xmlns="http://www.w3.org/2000/svg"
          p-id="4252"
          width="20"
          height="20"
          xmlns:xlink="http://www.w3.org/1999/xlink"
        >
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797"
            p-id="4253"
          ></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797"
            p-id="4254"
          ></path>
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in thinkOne" :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 < thinkOne.length - 1"
              />
              <img
                src="../../assets/images/icon/blue.png"
                alt=""
                v-if="index == thinkOne.length - 1"
                style="margin-right: 10px"
              />
            </span>
            <p class="txt-p">{{ item.txt }}</p>
          </div>
        </li>
      </ul>
      <div
        @click="showNext(thinkIndex)"
        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"
        />
        <svg
          xmlns="http://www.w3.org/2000/svg"
          xmlns:xlink="http://www.w3.org/1999/xlink"
          t="1710234570135"
          class="icon"
          viewBox="0 0 1024 1024"
          version="1.1"
          p-id="5067"
          width="15"
          height="15"
        >
          <path
            d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
            fill="#1296db"
            p-id="5068"
          />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db"
            p-id="5069"
          />
        </svg>
      </div>
    </el-dialog>
  </div>
</template>
 
<script>
import examinations from "@/components/examinations/index.vue";
import graffiti from "@/components/graffiti/index.vue";
import { getResourcePath } from "@/assets/methods/resources";
import {
  getCollectResource,
  setCollectResource,
} from "@/assets/methods/resources";
export default {
  name: "chapter-one",
  components: { examinations, graffiti },
  props: {
    showPageList: {
      type: Array,
      default: [],
    },
    questionData: {
      type: Object,
    },
  },
  async mounted() {
    const data = localStorage.getItem("math-chapterData");
    if (data) {
      this.chapterData = JSON.parse(data);
    }
    this.getPath();
    this.collectResourceList = await getCollectResource(
      this.config.activeBook.bookId
    );
  },
  data() {
    return {
      collectImg: require("../../assets/images/icon/heart.png"),
      collectCheck: require("../../assets/images/icon/heart-check.png"),
      isShowExampleOne: false,
      isShowExampleTwo: false,
      isShowExampleThree: false,
      isShowExampleFour: false,
      isShowExampleFive: false,
      dialogVisible: false,
      thinkingDialog: false,
      stepDialog: false,
      videoPath: "",
      stepIndex: 1,
      thinkIndex: 1,
      collectResourceList: [],
      chapterData: {
        isCollectImg: false,
        isCollectVideo: false,
        txtOne: "",
        txtTwo: "",
      },
      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,
        },
      ],
      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,
        },
      ],
      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: "",
            },
          ],
        },
      ],
    };
  },
  methods: {
    handleChapterData() {
      localStorage.setItem(
        "math-chapterData",
        JSON.stringify(this.chapterData)
      );
    },
    async getPath() {
      this.videoPath = await getResourcePath(
        "a28cd862d61b5df2201406b76e9f01b0"
      );
    },
    // getQuestionData() {
    //   axios
    //     .get(this.config.activeBook.resourceUrl + "/question.json")
    //     .then((res) => {
    //       let oldAnswer = localStorage.getItem(
    //         this.config.activeBook.name + "oldAnswerData"
    //       );
    //       if (oldAnswer) {
    //         oldAnswer = JSON.parse(oldAnswer);
    //         console.log("旧数据", oldAnswer);
    //         if (oldAnswer[9]) {
    //           for (let index = 0; index < res.data.data.length; index++) {
    //             const item = res.data.data[index];
    //             if (item.infoList.length) {
    //               for (
    //                 let cindex = 0;
    //                 cindex < item.infoList.length;
    //                 cindex++
    //               ) {
    //                 const citem = item.infoList[cindex];
    //                 const question = oldAnswer[9].find(
    //                   (ditem) => ditem.id == citem.id
    //                 );
    //                 if (question) {
    //                   citem.userAnswer = question.userAnswer;
    //                 }
    //               }
    //             }
    //           }
    //         }
    //       }
    //       this.questionData = res.data.data;
    //     });
    // },
    handleCollect(type) {
      if (type == "img") {
        this.handleCollectResource(
          "722FE833",
          "",
          "images/0101-1.jpg",
          "图片",
          "json",
          "图3-15"
        );
      } else if (type == "video") {
        this.handleCollectResource(
          "a28cd862d61b5df2201406b76e9f01b0",
          "a28cd862d61b5df2201406b76e9f01b0",
          "",
          "视频",
          "bits",
          "视频:判数函数奇偶性的方法和步骤"
        );
        // setCollectResource(this.config.activeBook.bookId,[])
      }
      this.handleChapterData();
    },
    openMathDiaolog() {
      this.dialogVisible = true;
    },
    openThinkingDialog() {
      this.thinkingDialog = true;
    },
    showNext(num) {
      const number = this.thinkOne.findIndex((item, index) => index == num);
      console.log(number);
      this.thinkOne[number].isShow = true;
      if (this.thinkIndex <= 2) {
        this.thinkIndex++;
      }
    },
    showNextChange(num) {
      const number = this.stepOne.findIndex((item, index) => index == num);
      this.stepOne[number].isShow = true;
      if (this.stepIndex < 2) {
        this.stepIndex++;
      }
    },
    //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);
      } else {
        list.push({
          id,
          md5,
          resourcePath,
          resourceType,
          source,
          resourceName,
        });
      }
      this.collectResourceList = list;
      setCollectResource(
        this.config.activeBook.bookId,
        this.collectResourceList
      );
    },
  },
};
</script>
 
<style lang="less" scoped>
p {
  font-size: 18px;
  text-align: justify;
}
 
.iframe-box {
  width: 100%;
  min-height: 800px;
  border: 1px solid #00a1e9;
  border-radius: 10px;
}
 
li {
  list-style: none;
}
 
.txt-p {
  margin-top: 0;
  padding: 10px 0;
}
 
.bottom-btn {
  display: flex;
  flex-direction: column;
  align-items: center;
  justify-content: center;
}
 
.step-num {
  position: relative;
 
  .step-num-box {
    position: absolute;
    top: 16px;
    left: 13px;
    color: #fff;
  }
}
 
.stepDialog {
}
</style>