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语数外复习资料.zip <link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89796422/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89796422/bg1.jpg"/><div class="c x1 y1 w2 h2"><div class="t m0 x0 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">-<span class="_ _0"> </span>1<span class="_ _0"> </span>-</div></div><div class="t m0 x2 h4 y3 ff2 fs1 fc0 sc1 ls0 ws0">数学<span class="_ _1"></span>概念与<span class="_ _1"></span>公式</div><div class="t m0 x3 h5 y4 ff2 fs2 fc0 sc1 ls0 ws0">初中基础知识：</div><div class="t m0 x3 h6 y5 ff2 fs3 fc0 sc0 ls0 ws0">1.<span class="_"> </span>相反数、绝对值、分数的运算；</div><div class="t m0 x3 h6 y6 ff2 fs3 fc0 sc0 ls0 ws0">2.<span class="_"> </span>因式分解：</div><div class="t m0 x4 h6 y7 ff2 fs3 fc0 sc0 ls0 ws0">提公因式：xy-3x=(y-3)x</div><div class="t m0 x4 h6 y8 ff2 fs3 fc0 sc0 ls0 ws0">十字相乘法<span class="_"> </span>如：</div><div class="c x5 y9 w3 h7"><div class="t m0 x6 h8 ya ff1 fs4 fc0 sc0 ls0 ws0">)<span class="_ _2"></span>2<span class="_ _3"></span>)(<span class="_ _4"></span>1<span class="_ _5"></span>3<span class="_ _6"></span>(<span class="_ _7"></span>2<span class="_ _8"></span>5<span class="_ _9"></span>3</div><div class="t m0 x7 h9 yb ff1 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x8 ha ya ff3 fs4 fc0 sc0 ls0 ws0"><span class="_ _a"></span><span class="_ _b"></span><span class="_ _c"></span><span class="_ _d"></span><span class="_ _e"> </span><span class="ff4">x<span class="_ _9"></span>x<span class="_ _f"></span>x<span class="_ _b"></span>x</span></div></div><div class="t m0 x4 h6 yc ff2 fs3 fc0 sc0 ls0 ws0">配方法<span class="_ _10"> </span>如：</div><div class="c x9 yd w4 hb"><div class="t m0 xa hc ye ff1 fs6 fc0 sc0 ls0 ws0">8</div><div class="t m0 xb hc yf ff1 fs6 fc0 sc0 ls0 ws0">25</div><div class="t m0 xc hc y10 ff1 fs6 fc0 sc0 ls0 ws0">)</div><div class="t m0 xd hc ye ff1 fs6 fc0 sc0 ls0 ws0">4</div><div class="t m0 xd hc yf ff1 fs6 fc0 sc0 ls0 ws0">1</div><div class="t m0 xe hc y10 ff1 fs6 fc0 sc0 ls0 ws0">(<span class="_ _11"></span>2<span class="_ _12"></span>3<span class="_ _13"></span>2</div><div class="t m0 xf hd y11 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _14"></span>2</div><div class="t m0 x10 he y10 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _b"></span><span class="_ _15"></span><span class="_ _7"></span><span class="_ _12"></span><span class="_ _16"> </span><span class="ff4">x<span class="_ _17"></span>x<span class="_ _18"></span>x</span></div></div><div class="t m0 x11 h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">公式法：<span class="_ _19"></span>（x+y）</div><div class="t m0 x12 hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x13 h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">=x</div><div class="t m0 x14 hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x15 h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">+2xy+y</div><div class="t m0 x16 hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x17 h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">(x-y)</div><div class="t m0 x18 hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x19 h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">=x</div><div class="t m0 x1a hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1b h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">-2xy+y</div><div class="t m0 x1c hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1d h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">x</div><div class="t m0 x1e hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1f h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">-y</div><div class="t m0 x20 hf y13 ff2 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m0 x21 h5 y12 ff2 fs2 fc0 sc0 ls0 ws0">=(x-y)(x+y)</div><div class="t m0 x3 h6 y14 ff2 fs3 fc0 sc0 ls0 ws0">3.<span class="_"> </span>一元一次方程、一元二次方程、二元一次方程组的解法：</div><div class="t m0 x3 h6 y15 ff2 fs3 fc0 sc0 ls0 ws0">（1）<span class="_"> </span>代入法</div><div class="t m0 x3 h6 y16 ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_"> </span>消元法</div><div class="t m0 x3 h6 y17 ff2 fs3 fc0 sc0 ls0 ws0">6.完全平方和（差）公式：</div><div class="c x22 y18 w5 h10"><div class="t m0 x23 hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _1a"></span>2<span class="_ _1b"></span>2</div><div class="t m0 xf he y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _1c"></span>(<span class="_ _1d"></span>2<span class="_ _1e"> </span><span class="ff4">b<span class="_ _7"></span>a<span class="_ _1f"></span>b<span class="_ _18"></span>ab<span class="_ _20"></span>a<span class="_ _21"> </span><span class="ff3"><span class="_ _18"></span><span class="_ _22"></span><span class="_ _9"></span></span></span></div></div><div class="c x24 y18 w6 h10"><div class="t m0 x23 hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _1a"></span>2<span class="_ _23"></span>2</div><div class="t m0 x4 he y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _1c"></span>(<span class="_ _24"></span>2<span class="_ _25"> </span><span class="ff4">b<span class="_ _26"></span>a<span class="_ _15"></span>b<span class="_ _18"></span>ab<span class="_ _27"></span>a<span class="_ _28"> </span><span class="ff3"><span class="_ _18"></span><span class="_ _22"></span><span class="_ _b"></span></span></span></div></div><div class="t m0 x3 h6 y1b ff2 fs3 fc0 sc0 ls0 ws0">7.平方差公式：</div><div class="c x25 y1c w7 h10"><div class="t m0 x26 hc y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _29"></span>)(<span class="_ _b"></span>(</div><div class="t m0 x27 hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _2a"></span>2</div><div class="t m0 xc he y1a ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _26"></span>a<span class="_ _2b"></span>b<span class="_ _7"></span>a<span class="_ _1f"></span>b<span class="_ _2c"></span>a<span class="_ _2d"> </span><span class="ff3"><span class="_ _2e"></span><span class="_ _18"></span><span class="_ _22"></span></span></div></div><div class="t m0 x3 h6 y1d ff2 fs3 fc0 sc0 ls0 ws0">8.立方和（差）公式：</div><div class="c x28 y1e w8 h10"><div class="t m0 x29 hc y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _2f"></span>)(<span class="_ _b"></span>(</div><div class="t m0 x2a hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _30"></span>2<span class="_ _31"></span>3<span class="_ _c"></span>3</div><div class="t m0 x2b he y1a ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _2c"></span>ab<span class="_ _29"></span>a<span class="_ _2b"></span>b<span class="_ _26"></span>a<span class="_ _32"></span>b<span class="_ _18"></span>a<span class="_ _33"> </span><span class="ff3"><span class="_ _34"></span><span class="_ _35"></span><span class="_ _18"></span><span class="_ _36"></span></span></div></div><div class="c x2c y1e w9 h10"><div class="t m0 x29 hc y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _2f"></span>)(<span class="_ _b"></span>(</div><div class="t m0 x2a hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _30"></span>2<span class="_ _31"></span>3<span class="_ _c"></span>3</div><div class="t m0 x2b he y1a ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _2c"></span>ab<span class="_ _29"></span>a<span class="_ _2b"></span>b<span class="_ _26"></span>a<span class="_ _32"></span>b<span class="_ _18"></span>a<span class="_ _33"> </span><span class="ff3"><span class="_ _36"></span><span class="_ _37"></span><span class="_ _18"></span><span class="_ _36"></span></span></div></div><div class="t m0 x2d h11 y1f ff2 fs9 fc0 sc1 ls0 ws0">第一章<span class="_"> </span>集合</div><div class="t m0 x3 h5 y20 ff2 fs3 fc0 sc0 ls0 ws0">1.<span class="_"> </span>构成集合的元素必须满足三要素：<span class="fs2">确定性、互<span class="_ _38"></span>异性、无序性<span class="_ _38"></span>。</span></div><div class="t m0 x3 h6 y21 ff2 fs3 fc0 sc0 ls0 ws0">2.<span class="_"> </span>集合的三种表示方法：列举法、<span class="sc1">描述法、</span>图像法（文氏图）<span class="_ _39"></span>。</div><div class="t m0 x3 h6 y22 ff2 fs3 fc0 sc0 ls0 ws0">注：</div><div class="c x2e y23 wa h12"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x30 h6 y22 ff2 fs3 fc0 sc0 ls0 ws0">描述法</div><div class="c x31 y25 wb h13"><div class="t m1 x32 h14 y26 ff5 fsa fc0 sc0 ls0 ws0"></div><div class="t m0 x33 h15 y27 ff1 fsa fc0 sc0 ls0 ws0">}<span class="_ _27"></span>,<span class="_ _3a"></span>|</div><div class="t m0 x34 h14 y28 ff5 fsa fc0 sc0 ls0 ws0"><span class="_ _3b"></span><span class="_ _3b"></span><span class="_ _1c"></span><span class="_ _3c"></span><span class="_ _3c"></span></div><div class="t m0 x35 h16 y29 ff2 fsb fc0 sc0 ls0 ws0">取值范围<span class="_ _3d"></span>元素性质</div><div class="t m0 x36 h16 y2a ff2 fsb fc0 sc0 ls0 ws0">元素</div><div class="t m0 x37 h17 y27 ff2 fsa fc0 sc0 ls0 ws0">｛<span class="_ _3e"> </span><span class="ff3"><span class="_ _7"></span><span class="_ _15"></span><span class="_ _3c"></span><span class="_ _3f"> </span><span class="ff4">x<span class="_ _40"></span>x<span class="_ _41"></span>x</span></span></div></div><div class="t m0 x38 h6 y22 ff2 fs3 fc0 sc0 ls0 ws0">；另重点类型如：</div><div class="c x39 y2b wc h10"><div class="t m0 x2a h18 y1a ff2 fs6 fc0 sc0 ls0 ws0">｝<span class="_ _42"></span>｛<span class="_ _43"> </span><span class="ff1">]<span class="_ _44"></span>3<span class="_ _45"></span>,<span class="_ _46"></span>1<span class="_ _47"></span>(<span class="_ _2a"></span>,<span class="_ _46"></span>1<span class="_ _48"></span>3<span class="_ _49"></span>|<span class="_ _2"></span>y</span></div><div class="t m0 x3a hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3b he y1a ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _4a"></span><span class="_ _4b"></span><span class="_ _5"></span><span class="_ _22"></span><span class="_ _4c"> </span><span class="ff4">x<span class="_ _8"></span>x<span class="_ _4d"></span>x<span class="_ _12"></span>y</span></div></div><div class="t m0 x3 h6 y2c ff2 fs3 fc0 sc0 ls0 ws0">3.<span class="_"> </span>常用数集：</div><div class="c x3c y2d wd h19"><div class="t m0 x2f hc y2e ff4 fs6 fc0 sc0 ls0 ws0">N</div></div><div class="t m0 x3d h6 y2c ff2 fs3 fc0 sc0 ls0 ws0">（自然数集）<span class="_ _39"></span>、</div><div class="c x3e y2f we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">Z</div></div><div class="t m0 x16 h6 y2c ff2 fs3 fc0 sc0 ls0 ws0">（整数集）<span class="_ _39"></span>、</div><div class="c x18 y31 we h1b"><div class="t m0 x2f hc y32 ff4 fs6 fc0 sc0 ls0 ws0">Q</div></div><div class="t m0 x3f h6 y2c ff2 fs3 fc0 sc0 ls0 ws0">（有理数集）<span class="_ _39"></span>、</div><div class="c x40 y2f we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">R</div></div><div class="t m0 x41 h6 y2c ff2 fs3 fc0 sc0 ls0 ws0">（实数集）<span class="_ _39"></span>、</div><div class="c x42 y2d wf h1b"><div class="t m0 x43 hd y33 ff1 fs7 fc0 sc0 ls0 ws0">*</div><div class="t m0 x2f hc y34 ff4 fs6 fc0 sc0 ls0 ws0">N</div></div><div class="t m0 x44 h6 y2c ff2 fs3 fc0 sc0 ls0 ws0">（正整</div><div class="t m0 x45 h6 y35 ff2 fs3 fc0 sc0 ls0 ws0">数集）<span class="_ _39"></span>、</div><div class="c x46 y36 wf h1c"><div class="t m0 x32 h1d y37 ff3 fs7 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f hc y24 ff4 fs6 fc0 sc0 ls0 ws0">Z</div></div><div class="t m0 x47 h6 y35 ff2 fs3 fc0 sc0 ls0 ws0">（正整数集）</div><div class="t m0 x3 h6 y38 ff2 fs3 fc0 sc0 ls0 ws0">4.<span class="_"> </span>元素与集合、集合与集合之间的关系：</div><div class="t m0 x3 h6 y39 ff2 fs3 fc0 sc0 ls0 ws0">（1）<span class="_"> </span>元素与集合是“</div><div class="c x28 y3a w10 h1e"><div class="t m0 x0 he y3b ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x48 h6 y39 ff2 fs3 fc0 sc0 ls0 ws0">”与“</div><div class="c x49 y3c w11 h1f"><div class="t m0 x0 he y3d ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x38 h6 y39 ff2 fs3 fc0 sc0 ls0 ws0">”的关系。</div><div class="t m0 x3 h6 y3e ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_"> </span>集合与集合是“</div><div class="c x28 y3f we h1f"><div class="t m0 x2f he y40 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x4a h6 y3e ff2 fs3 fc0 sc0 ls0 ws0">”<span class="_"> </span>“<span class="_ _4e"> </span>”<span class="_ _39"></span>“</div><div class="c x4b y41 w11 h20"><div class="t m0 x2f he y42 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x4c h6 y3e ff2 fs3 fc0 sc0 ls0 ws0">”<span class="_ _39"></span>“</div><div class="c x4d y43 we h21"><div class="t m0 x2f he y44 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x4e he y45 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x4f h6 y3e ff2 fs3 fc0 sc0 ls0 ws0">”的关系。</div><div class="t m0 x3 h6 y46 ff2 fs3 fc0 sc1 ls0 ws0">注：<span class="_ _4f"></span><span class="sc0">（1）<span class="_ _50"></span>空集是任何集合的子集，<span class="_ _50"></span>任何非空集合的真子集。<span class="_ _4f"></span>（做题时多考虑</span></div><div class="c x50 y47 w11 h1b"><div class="t m2 x51 h22 y32 ff3 fsc fc0 sc0 ls0 ws0"></div></div><div class="t m0 x52 h6 y46 ff2 fs3 fc0 sc0 ls0 ws0">是否满足题意）</div><div class="t m0 x3 h6 y48 ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_ _50"></span>一个集合含有</div><div class="c x53 y49 w11 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x54 h6 y48 ff2 fs3 fc0 sc0 ls0 ws0">个元素，<span class="_ _50"></span>则它的子集有</div><div class="c x55 y4b wd h1c"><div class="t m0 x56 hd y37 ff4 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m0 x2f hc y24 ff1 fs6 fc0 sc0 ls0 ws0">2</div></div><div class="t m0 x57 h6 y48 ff2 fs3 fc0 sc0 ls0 ws0">个，<span class="_ _50"></span>真子集有</div><div class="c x58 y4b w12 h1c"><div class="t m0 x59 he y24 ff1 fs6 fc0 sc0 ls0 ws0">1<span class="_ _48"></span>2<span class="_ _51"> </span><span class="ff3"></span></div><div class="t m0 x56 hd y37 ff4 fs7 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x5a h6 y48 ff2 fs3 fc0 sc0 ls0 ws0">个，<span class="_ _50"></span>非空真子集有</div><div class="c x5b y4b w13 h1c"><div class="t m0 x5c he y24 ff1 fs6 fc0 sc0 ls0 ws0">2<span class="_ _5"></span>2<span class="_ _51"> </span><span class="ff3"></span></div><div class="t m0 x56 hd y37 ff4 fs7 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x3 h6 y4c ff2 fs3 fc0 sc0 ls0 ws0">个。</div><div class="t m0 x3 h6 y4d ff2 fs3 fc0 sc0 ls0 ws0">5.<span class="_"> </span><span class="sc1">集合的基本运算</span>（用描述法表示的集合的运算尽量用画数轴的方法）</div><div class="t m0 x3 h6 y4e ff2 fs3 fc0 sc0 ls0 ws0">（1）</div><div class="c x5d y4f w14 h24"><div class="t m0 x5e he y50 ff1 fs6 fc0 sc0 ls0 ws0">}<span class="_ _52"></span>|<span class="_ _53"></span>{<span class="_ _1e"> </span><span class="ff4">B<span class="_ _41"></span>x<span class="_ _54"></span>A<span class="_ _c"></span>x<span class="_ _55"></span>x<span class="_ _22"></span>B<span class="_ _56"></span>A<span class="_ _57"> </span><span class="ff3"><span class="_ _58"></span><span class="_ _59"></span><span class="_ _5a"> </span><span class="ff2">且<span class="_ _5b"></span><span class="ff5"></span></span></span></span></div></div><div class="t m0 x5f h6 y4e ff2 fs3 fc0 sc0 ls0 ws0">：</div><div class="c x60 y51 we h1a"><div class="t m0 x61 hc y30 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x62 h6 y4e ff2 fs3 fc0 sc0 ls0 ws0">与</div><div class="c x63 y51 we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">B</div></div><div class="t m0 x64 h6 y4e ff2 fs3 fc0 sc0 ls0 ws0">的公共元素（相同元素）组成的集合</div><div class="t m0 x65 h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">（2）</div><div class="c x4 y53 w14 h24"><div class="t m0 x5e he y50 ff1 fs6 fc0 sc0 ls0 ws0">}<span class="_ _52"></span>|<span class="_ _53"></span>{<span class="_ _25"> </span><span class="ff4">B<span class="_ _41"></span>x<span class="_ _54"></span>A<span class="_ _5c"></span>x<span class="_ _55"></span>x<span class="_ _8"></span>B<span class="_ _56"></span>A<span class="_ _57"> </span><span class="ff3"><span class="_ _58"></span><span class="_ _59"></span><span class="_ _5a"> </span><span class="ff2">或<span class="_ _5b"></span><span class="ff5"></span></span></span></span></div></div><div class="t m0 x66 h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">：</div><div class="c x67 y54 we h1a"><div class="t m0 x61 hc y30 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x68 h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">与</div><div class="c x69 y54 we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">B</div></div><div class="t m0 x6a h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">的所有元素组成的集合（相同元素只写一次）<span class="_ _39"></span>。</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89796422/bg2.jpg"><div class="c x3 y1 w2 h2"><div class="t m0 x0 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">-<span class="_ _0"> </span>2<span class="_ _0"> </span>-</div></div><div class="t m0 x3 h6 y55 ff2 fs3 fc0 sc0 ls0 ws0">（3）</div><div class="c x5d y56 w15 h10"><div class="t m0 x6b hc y57 ff4 fs6 fc0 sc0 ls0 ws0">A<span class="_ _26"></span>C</div><div class="t m0 x6c hd y3d ff4 fs7 fc0 sc0 ls0 ws0">U</div></div><div class="t m0 x6d h6 y55 ff2 fs3 fc0 sc0 ls0 ws0">：</div><div class="c x2a y58 w16 h19"><div class="t m0 x51 hc y2e ff4 fs6 fc0 sc0 ls0 ws0">U</div></div><div class="t m0 x6e h6 y55 ff2 fs3 fc0 sc0 ls0 ws0">中元素去掉</div><div class="c x6f y59 we h12"><div class="t m0 x61 hc y24 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x70 h6 y55 ff2 fs3 fc0 sc0 ls0 ws0">中元素剩下的元素组成的集合。</div><div class="t m0 x3 h6 y5a ff2 fs3 fc0 sc1 ls0 ws0">注：</div><div class="c x2e y5b w17 h10"><div class="t m0 x71 hc y57 ff4 fs6 fc0 sc0 ls0 ws0">B<span class="_ _5d"></span>C<span class="_ _56"></span>A<span class="_ _26"></span>C<span class="_ _1c"></span>B<span class="_ _5e"></span>A<span class="_ _48"></span>C</div><div class="t m0 x26 hd y3d ff4 fs7 fc0 sc0 ls0 ws0">U<span class="_ _5f"></span>U<span class="_ _60"></span>U</div><div class="t m0 x11 he y57 ff5 fs6 fc0 sc0 ls0 ws0"><span class="_ _61"></span><span class="_ _62"> </span><span class="ff3"><span class="_ _63"></span><span class="ff1">)<span class="_ _64"></span>(</span></span></div></div><div class="c x67 y5b w17 h10"><div class="t m0 x71 hc y57 ff4 fs6 fc0 sc0 ls0 ws0">B<span class="_ _5d"></span>C<span class="_ _56"></span>A<span class="_ _26"></span>C<span class="_ _1c"></span>B<span class="_ _5e"></span>A<span class="_ _48"></span>C</div><div class="t m0 x26 hd y3d ff4 fs7 fc0 sc0 ls0 ws0">U<span class="_ _5f"></span>U<span class="_ _60"></span>U</div><div class="t m0 x11 he y57 ff5 fs6 fc0 sc0 ls0 ws0"><span class="_ _61"></span><span class="_ _62"> </span><span class="ff3"><span class="_ _63"></span><span class="ff1">)<span class="_ _64"></span>(</span></span></div></div><div class="t m0 x3 h6 y5 ff2 fs3 fc0 sc0 ls0 ws0">6.<span class="_"> </span>逻辑联结词：</div><div class="t m0 x3 h6 y6 ff2 fs3 fc0 sc0 ls0 ws0">且（</div><div class="c x2e y5c wa h1e"><div class="t m0 x2f he y3b ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x30 h6 y6 ff2 fs3 fc0 sc0 ls0 ws0">）<span class="_ _39"></span>、或（</div><div class="c x47 y5c wa h1e"><div class="t m0 x2f he y3b ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x72 h6 y6 ff2 fs3 fc0 sc0 ls0 ws0">）非（</div><div class="c x73 y5d we h20"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x14 h6 y6 ff2 fs3 fc0 sc0 ls0 ws0">）如果……那么……（</div><div class="c x74 y5e w18 h1f"><div class="t m0 x51 he y3d ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x75 h6 y6 ff2 fs3 fc0 sc0 ls0 ws0">）</div><div class="t m0 x3 h6 y7 ff2 fs3 fc0 sc0 ls0 ws0">量词：存在（</div><div class="c x76 y5f w10 h1f"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x77 h6 y7 ff2 fs3 fc0 sc0 ls0 ws0">）<span class="_ _65"> </span>任意（</div><div class="c x78 y5f we h1a"><div class="t m0 x51 he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x79 h6 y7 ff2 fs3 fc0 sc0 ls0 ws0">）</div><div class="t m0 x3 h6 y60 ff2 fs3 fc0 sc0 ls0 ws0">真值表：</div><div class="c x3 y61 w19 h1a"><div class="t m0 x7a he y62 ff4 fs6 fc0 sc0 ls0 ws0">q<span class="_ _12"></span>p<span class="_ _66"> </span><span class="ff3"></span></div></div><div class="t m0 x5d h6 y63 ff2 fs3 fc0 sc0 ls0 ws0">：其中一个为假则为假，全部为真才为真；</div><div class="c x3 y64 w19 h1a"><div class="t m0 x7a he y62 ff4 fs6 fc0 sc0 ls0 ws0">q<span class="_ _12"></span>p<span class="_ _0"> </span><span class="ff3"></span></div></div><div class="t m0 x5d h6 y65 ff2 fs3 fc0 sc0 ls0 ws0">：其中一个为真则为真，全部为假才为假；</div><div class="c x3 y66 w1a h1a"><div class="t m0 x7b he y62 ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _67"></span><span class="ff3"></span></div></div><div class="t m0 x7c h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">：与</div><div class="c x7d y66 we h1a"><div class="t m0 x61 hc y62 ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 xb h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">的真假相反。</div><div class="t m0 x3 h6 y15 ff2 fs3 fc0 sc0 ls0 ws0">（同为真时<span class="_ _50"></span>“且”<span class="_ _50"></span>为真，<span class="_ _50"></span>同为假时<span class="_ _50"></span>“或”<span class="_ _50"></span>为假，<span class="_ _50"></span>真的<span class="_ _50"></span>“非”<span class="_ _50"></span>为假，<span class="_ _50"></span>假的<span class="_ _50"></span>“非”<span class="_ _50"></span>为真；<span class="_ _50"></span>真<span class="_ _50"></span>“<span class="_ _38"></span>推”</div><div class="t m0 x3 h6 y16 ff2 fs3 fc0 sc0 ls0 ws0">假为假，假“推”真假均为真。<span class="_ _39"></span>）</div><div class="t m0 x3 h6 y68 ff2 fs3 fc0 sc0 ls0 ws0">7.<span class="_"> </span>命题的非</div><div class="t m0 x3 h6 y69 ff2 fs3 fc0 sc0 ls0 ws0">（1）是</div><div class="c x23 y6a w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xa h6 y69 ff2 fs3 fc0 sc0 ls0 ws0">不是</div><div class="t m0 x3 h6 y6b ff2 fs3 fc0 sc0 ls0 ws0">都是</div><div class="c x2e y6c w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x26 h6 y6b ff2 fs3 fc0 sc0 ls0 ws0">不都是（至少有一个不是）</div><div class="t m0 x3 h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">（2）</div><div class="c x5d y6e w10 h1f"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x7e h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">……，使得</div><div class="c x7f y6f we h1a"><div class="t m0 x61 hc y62 ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x80 h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">成立</div><div class="c x14 y70 w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x81 h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">对于</div><div class="c x82 y71 we h1a"><div class="t m0 x51 he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x83 h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">……，都有</div><div class="c x84 y6f w1b h1a"><div class="t m0 x7b he y62 ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _67"></span><span class="ff3"></span></div></div><div class="t m0 x1a h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">成立。</div><div class="t m0 x3 h6 y72 ff2 fs3 fc0 sc0 ls0 ws0">对于</div><div class="c x2e y73 we h1a"><div class="t m0 x51 he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x4 h6 y72 ff2 fs3 fc0 sc0 ls0 ws0">……，都有</div><div class="c x85 y74 we h1a"><div class="t m0 x61 hc y62 ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x86 h6 y72 ff2 fs3 fc0 sc0 ls0 ws0">成立</div><div class="c x4a y75 w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x87 y76 w10 h1f"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x88 h6 y72 ff2 fs3 fc0 sc0 ls0 ws0">……，使得</div><div class="c x4d y74 w1b h1a"><div class="t m0 x7b he y62 ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _67"></span><span class="ff3"></span></div></div><div class="t m0 x89 h6 y72 ff2 fs3 fc0 sc0 ls0 ws0">成立</div><div class="t m0 x3 h6 y77 ff2 fs3 fc0 sc0 ls0 ws0">（3）</div><div class="c x5d y78 w1c h1b"><div class="t m0 x8a he y32 ff4 fs6 fc0 sc0 ls0 ws0">q<span class="_ _68"></span>p<span class="_ _a"></span>q<span class="_ _12"></span>p<span class="_ _69"> </span><span class="ff3"><span class="_ _6a"></span><span class="_ _12"></span><span class="_ _6b"></span><span class="_ _34"></span><span class="_ _5"></span><span class="_ _6c"> </span><span class="ff1">)<span class="_ _32"></span>(</span></span></div></div><div class="c x8b y78 w1c h1b"><div class="t m0 x8a he y32 ff4 fs6 fc0 sc0 ls0 ws0">q<span class="_ _68"></span>p<span class="_ _a"></span>q<span class="_ _12"></span>p<span class="_ _69"> </span><span class="ff3"><span class="_ _6a"></span><span class="_ _12"></span><span class="_ _6b"></span><span class="_ _36"></span><span class="_ _5"></span><span class="_ _6d"> </span><span class="ff1">)<span class="_ _32"></span>(</span></span></div></div><div class="t m0 x3 h6 y79 ff2 fs3 fc0 sc0 ls0 ws0">8.<span class="_"> </span>充分必要条件</div><div class="c x3 y7a wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x8c y7b we h1a"><div class="t m0 x61 hc y62 ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x8d h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">是</div><div class="c x30 y7b w11 h1a"><div class="t m0 x2f hc y62 ff4 fs6 fc0 sc0 ls0 ws0">q</div></div><div class="t m0 x10 h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">的……条件</div><div class="c x8e y7b we h1a"><div class="t m0 x61 hc y62 ff4 fs6 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x6f h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">是条件，</div><div class="c x4b y7b w10 h1a"><div class="t m0 x2f hc y62 ff4 fs6 fc0 sc0 ls0 ws0">q</div></div><div class="t m0 x4c h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">是结论</div><div class="c x3 y7d w1d h25"><div class="t m0 x61 hc y7e ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _6e"> </span>q</div><div class="t m0 x8f he y7f ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x90 he y80 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x8f h18 y81 ff2 fs6 fc0 sc0 ls0 ws0">充分</div><div class="t m0 x7b h18 y82 ff2 fs6 fc0 sc0 ls0 ws0">不必要</div></div><div class="c x91 y83 w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x92 y84 w1e h24"><div class="t m0 x93 h18 y50 ff2 fs6 fc0 sc0 ls0 ws0">的充分不必要条件<span class="_ _6f"></span>是<span class="ff4">q<span class="_ _70"></span>p</span></div></div><div class="t m0 x94 h6 y85 ff2 fs3 fc0 sc0 ls0 ws0">（充分条件）</div><div class="c x3 y86 w1d h25"><div class="t m0 x61 hc y7e ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _6e"> </span>q</div><div class="t m0 x8f he y87 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x90 he y88 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x7b h18 y89 ff2 fs6 fc0 sc0 ls0 ws0">不充分</div><div class="t m0 x8f h18 y8a ff2 fs6 fc0 sc0 ls0 ws0">必要</div></div><div class="c x91 y8b w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x92 y8c w1e h24"><div class="t m0 x93 h18 y50 ff2 fs6 fc0 sc0 ls0 ws0">的必要不充分条件<span class="_ _6f"></span>是<span class="ff4">q<span class="_ _70"></span>p</span></div></div><div class="t m0 x94 h6 y8d ff2 fs3 fc0 sc0 ls0 ws0">（必要条件）</div><div class="c x3 y8e w1f h25"><div class="t m0 x61 hc y7e ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _71"> </span>q</div><div class="t m0 x32 he y87 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x32 he y88 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x32 h18 y89 ff2 fs6 fc0 sc0 ls0 ws0">充分</div><div class="t m0 x32 h18 y8a ff2 fs6 fc0 sc0 ls0 ws0">必要</div></div><div class="c x77 y8f w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x95 y90 w20 h24"><div class="t m0 x93 h18 y50 ff2 fs6 fc0 sc0 ls0 ws0">的充分必要条件<span class="_ _72"></span>是<span class="ff4">q<span class="_ _70"></span>p</span></div></div><div class="t m0 x96 h6 y91 ff2 fs3 fc0 sc0 ls0 ws0">(充要条件)</div><div class="c x3 y92 w1d h25"><div class="t m0 x61 hc y7e ff4 fs6 fc0 sc0 ls0 ws0">p<span class="_ _6e"> </span>q</div><div class="t m0 x8f he y7f ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x8f he y93 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x7b h18 y81 ff2 fs6 fc0 sc0 ls0 ws0">不充分</div><div class="t m0 x7b h18 y82 ff2 fs6 fc0 sc0 ls0 ws0">不必要</div></div><div class="c x91 y94 w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x92 y95 w21 h24"><div class="t m0 x47 h18 y50 ff2 fs6 fc0 sc0 ls0 ws0">件<span class="_ _73"></span>的既不充分也不必要条<span class="_ _74"></span>是<span class="ff4">q<span class="_ _70"></span>p</span></div></div><div class="t m0 x2 h4 y96 ff2 fs1 fc0 sc1 ls0 ws0">第二<span class="_ _1"></span>章<span class="_ _75"> </span>不等<span class="_ _1"></span>式</div><div class="t m0 x3 h6 y4d ff2 fs3 fc0 sc0 ls0 ws0">1.<span class="_"> </span>不等式的基本性质：</div><div class="t m0 x3 h6 y97 ff2 fs3 fc0 sc1 ls0 ws0">注：<span class="_ _39"></span><span class="sc0">（1）比较两个实数的大小一般用比较差的方法；另外还可以用平方法、倒数法如：</span></div><div class="c x3 y98 w22 h10"><div class="t m0 x31 he y40 ff1 fs6 fc0 sc0 ls0 ws0">2008<span class="_ _76"></span>2009<span class="_ _77"></span>2009<span class="_ _76"></span>2010<span class="_ _78"> </span><span class="ff3"><span class="_ _79"></span><span class="_ _7a"> </span><span class="ff2">与</span></span></div></div><div class="t m0 x97 h6 y99 ff2 fs3 fc0 sc0 ls0 ws0">（倒数法）等。</div><div class="t m0 x3 h6 y9a ff2 fs3 fc0 sc0 ls0 ws0">（2）不等式两边同时乘以负数要变号！<span class="_ _39"></span>！</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89796422/bg3.jpg"><div class="c x1 y1 w2 h2"><div class="t m0 x0 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">-<span class="_ _0"> </span>3<span class="_ _0"> </span>-</div></div><div class="t m0 x3 h6 y9b ff2 fs3 fc0 sc0 ls0 ws0">（3）<span class="sc1">同向</span>的不等式可以相<span class="sc1">加</span>（不能相减）<span class="_ _39"></span>，<span class="sc1">同正的同向</span>不等式可以相乘。</div><div class="t m0 x3 h5 y9c ff2 fs3 fc0 sc0 ls0 ws0">2.<span class="_"> </span><span class="fs2 sc1">重要的不等式：<span class="_ _19"></span><span class="fs3 sc0">（</span></span></div><div class="c x98 y9d wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x4a h6 y9c ff2 fs3 fc0 sc1 ls0 ws0">均值定理<span class="sc0">）</span></div><div class="t m0 x3 h6 y9e ff2 fs3 fc0 sc0 ls0 ws0">（1）</div><div class="c x5d y9f w23 h1b"><div class="t m0 x99 hc ya0 ff4 fs6 fc0 sc0 ls0 ws0">ab<span class="_ _40"></span>b<span class="_ _5"></span>a<span class="_ _7b"> </span><span class="ff1">2</span></div><div class="t m0 x27 hd y33 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _56"></span>2</div><div class="t m0 x9a he ya0 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _36"></span></div></div><div class="t m0 x7f h6 y9e ff2 fs3 fc0 sc0 ls0 ws0">，当且仅当</div><div class="c x9b y9f w24 h21"><div class="t m0 x9c he ya1 ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _54"></span>a<span class="_ _7c"> </span><span class="ff3"></span></div></div><div class="t m0 x4b h6 y9e ff2 fs3 fc0 sc0 ls0 ws0">时，等号成立。</div><div class="t m0 x3 h6 ya2 ff2 fs3 fc0 sc0 ls0 ws0">（2）</div><div class="c x5d ya3 w25 h26"><div class="t m0 x23 hc ya4 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _7d"></span>,<span class="_ _63"></span>(<span class="_ _d"></span>2</div><div class="t m0 x4 h1d ya5 ff3 fs7 fc0 sc0 ls0 ws0"></div><div class="t m0 x9d he ya4 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _76"></span><span class="_ _12"></span><span class="_ _7e"> </span><span class="ff4">R<span class="_ _c"></span>b<span class="_ _53"></span>a<span class="_ _26"></span>ab<span class="_ _7f"></span>b<span class="_ _7"></span>a</span></div></div><div class="t m0 x9e h6 ya2 ff2 fs3 fc0 sc0 ls0 ws0">，当且仅当</div><div class="c x9f ya6 w26 h19"><div class="t m0 x9c he y2e ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _54"></span>a<span class="_ _7c"> </span><span class="ff3"></span></div></div><div class="t m0 x94 h6 ya2 ff2 fs3 fc0 sc0 ls0 ws0">时，等号成立。</div><div class="t m0 x3 h6 ya7 ff2 fs3 fc0 sc0 ls0 ws0">（3）</div><div class="c x5d ya8 w8 h26"><div class="t m0 x29 hc ya4 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _3a"></span>,<span class="_ _80"></span>,<span class="_ _63"></span>(<span class="_ _9"></span>3</div><div class="t m0 xa0 h1d ya5 ff3 fs7 fc0 sc0 ls0 ws0"></div><div class="t m0 xa1 he ya4 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _81"></span><span class="_ _70"></span><span class="_ _70"></span><span class="_ _82"> </span><span class="ff4">R<span class="_ _41"></span>c<span class="_ _83"></span>b<span class="_ _53"></span>a<span class="_ _18"></span>abc<span class="_ _84"></span>c<span class="_ _5d"></span>b<span class="_ _7"></span>a</span></div></div><div class="t m0 x2 h6 ya7 ff2 fs3 fc0 sc0 ls0 ws0">，当且仅当</div><div class="c xa2 ya9 w27 h19"><div class="t m0 xa3 he y2e ff4 fs6 fc0 sc0 ls0 ws0">c<span class="_ _70"></span>b<span class="_ _54"></span>a<span class="_ _85"> </span><span class="ff3"><span class="_ _41"></span></span></div></div><div class="t m0 xa4 h6 ya7 ff2 fs3 fc0 sc0 ls0 ws0">时，等号成立。</div><div class="t m0 x3 h6 yc ff2 fs3 fc0 sc0 ls0 ws0">注：</div><div class="c x2e yd w26 hb"><div class="t m0 x32 hc ye ff1 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9c he yf ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _7"></span>a<span class="_ _66"> </span><span class="ff3"></span></div></div><div class="t m0 xa5 h6 yc ff2 fs3 fc0 sc0 ls0 ws0">（算术平均数）</div><div class="c x14 yaa w11 h1f"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x87 yab w28 h10"><div class="t m0 x6c hc y40 ff4 fs6 fc0 sc0 ls0 ws0">ab</div></div><div class="t m0 xa6 h6 yc ff2 fs3 fc0 sc0 ls0 ws0">（几何平均数）</div><div class="t m0 x3 h6 yac ff2 fs3 fc0 sc0 ls0 ws0">3.<span class="_"> </span>一元一次不等式的解法</div><div class="t m0 x3 h6 yad ff2 fs3 fc0 sc0 ls0 ws0">4.<span class="_"> </span>一元二次不等式的解法</div><div class="t m0 x3 h6 y14 ff2 fs3 fc0 sc0 ls0 ws0">（1）<span class="_"> </span>保证二次项系数为正</div><div class="t m0 x3 h6 y15 ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_"> </span>分解因式（十字相乘法、提取公因式、求根公式法）<span class="_ _39"></span>，目的是求根：</div><div class="t m0 x3 h6 y16 ff2 fs3 fc0 sc0 ls0 ws0">（3）<span class="_"> </span>定解：<span class="_ _39"></span>（口诀）大于两根之外，大于大的，小于小的；</div><div class="t m0 x28 h6 y68 ff2 fs3 fc0 sc0 ls0 ws0">小于两根之间</div><div class="t m0 x3 h6 y69 ff2 fs3 fc0 sc1 ls0 ws0">注：<span class="sc0">若</span></div><div class="c x4 y6a w29 h1c"><div class="t m0 xa7 he y3d ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _86"></span>0<span class="_ _85"> </span><span class="ff3"><span class="_ _47"></span><span class="_ _32"></span><span class="_ _47"></span><span class="_ _87"> </span><span class="ff2">或</span></span></div></div><div class="t m0 xa8 h6 y69 ff2 fs3 fc0 sc0 ls0 ws0">，用配方的方法确定不等式的解集。</div><div class="t m0 x3 h6 y6b ff2 fs3 fc0 sc0 ls0 ws0">5.<span class="_"> </span>绝对值不等式的解法</div><div class="t m0 x3 h6 yae ff2 fs3 fc0 sc0 ls0 ws0">若</div><div class="c xa9 yaf w26 h19"><div class="t m0 x9c he y2e ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _88"></span><span class="ff3"><span class="_ _83"></span><span class="ff4">a</span></span></div></div><div class="t m0 xaa h6 yae ff2 fs3 fc0 sc0 ls0 ws0">，则</div><div class="c xab yb0 w2a h27"><div class="t m0 x2f he yb1 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he yb2 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he yb3 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x23 he yb4 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _53"></span><span class="_ _40"></span><span class="_ _1c"></span><span class="_ _d"></span></div><div class="t m0 x5d he yb5 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _41"></span><span class="_ _5d"></span><span class="_ _5d"></span><span class="_ _d"></span></div><div class="t m0 x8 hc yb4 ff4 fs6 fc0 sc0 ls0 ws0">a<span class="_ _d"></span>x<span class="_ _26"></span>a<span class="_ _12"></span>x<span class="_ _d"></span>a<span class="_ _5c"></span>x</div><div class="t m0 x7e hc yb5 ff4 fs6 fc0 sc0 ls0 ws0">a<span class="_ _12"></span>x<span class="_ _54"></span>a<span class="_ _a"></span>a<span class="_ _5c"></span>x</div><div class="t m0 xa9 h18 yb4 ff2 fs6 fc0 sc0 ls0 ws0">或<span class="_ _89"></span><span class="ff1">|<span class="_ _83"></span>|</span></div><div class="t m0 xac hc yb5 ff1 fs6 fc0 sc0 ls0 ws0">|<span class="_ _83"></span>|</div></div><div class="t m0 x3 h6 yb6 ff2 fs3 fc0 sc0 ls0 ws0">6.<span class="_"> </span>分式不等式的解法：与二次不等式的解法相同。注：分母不能为<span class="_ _8a"> </span>0.</div><div class="t m0 xad h4 yb7 ff2 fs1 fc0 sc1 ls0 ws0">第三<span class="_ _1"></span>章<span class="_ _75"> </span>函数</div><div class="t m0 x3 h6 y79 ff2 fs3 fc0 sc0 ls0 ws0">1.<span class="_"> </span>映射:</div><div class="t m0 x3 h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">一般地，设</div><div class="c x46 yb8 w2b h21"><div class="t m0 x7a h18 ya1 ff4 fs6 fc0 sc0 ls0 ws0">B<span class="_ _2a"></span>A<span class="ff2">、</span></div></div><div class="t m0 x3d h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">是两个集合，如果按照某种对应法则</div><div class="c xae y7b we h1b"><div class="t m0 x4e hc y32 ff4 fs6 fc0 sc0 ls0 ws0">f</div></div><div class="t m0 xaf h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">，对于集合</div><div class="c xb0 y7a we h1a"><div class="t m0 x61 hc y30 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 xb1 h6 y7c ff2 fs3 fc0 sc0 ls0 ws0">中的任何一个元素，</div><div class="t m0 x3 h6 yb9 ff2 fs3 fc0 sc0 ls0 ws0">在集合</div><div class="c x4 yba we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">B</div></div><div class="t m0 xa1 h6 yb9 ff2 fs3 fc0 sc0 ls0 ws0">中都有惟一的元素和它对应，这样的对应叫做从集合</div><div class="c xb2 yba we h1a"><div class="t m0 x61 hc y30 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x1e h6 yb9 ff2 fs3 fc0 sc0 ls0 ws0">到集合</div><div class="c xb3 yba we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">B</div></div><div class="t m0 xb4 h6 yb9 ff2 fs3 fc0 sc0 ls0 ws0">的映射，记作：</div><div class="c x3 ybb w2c h1b"><div class="t m0 xb5 he y32 ff4 fs6 fc0 sc0 ls0 ws0">B<span class="_ _8b"></span>A<span class="_ _3c"></span>f<span class="_ _8c"> </span><span class="ff3"><span class="_ _48"></span><span class="ff1">:</span></span></div></div><div class="t m0 x5e h6 ybc ff2 fs3 fc0 sc0 ls0 ws0">。</div><div class="t m0 x3 h6 ybd ff2 fs3 fc0 sc0 ls0 ws0">注：理解原象与象及其应用。</div><div class="t m0 x3 h6 ybe ff2 fs3 fc0 sc0 ls0 ws0">（1）</div><div class="c x5d ybf we h1a"><div class="t m0 x61 hc y30 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x23 h6 ybe ff2 fs3 fc0 sc0 ls0 ws0">中每一个元素必有惟一的象；</div><div class="t m0 x3 h6 y38 ff2 fs3 fc0 sc0 ls0 ws0">（2）对于</div><div class="c x5e yc0 we h1a"><div class="t m0 x61 hc y30 ff4 fs6 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 xb6 h6 y38 ff2 fs3 fc0 sc0 ls0 ws0">中的不同的元素，在</div><div class="c x60 yc0 we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">B</div></div><div class="t m0 x62 h6 y38 ff2 fs3 fc0 sc0 ls0 ws0">中可以有相同的象；</div><div class="t m0 x3 h6 y39 ff2 fs3 fc0 sc0 ls0 ws0">（3）允许</div><div class="c x5e y3a we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">B</div></div><div class="t m0 xb6 h6 y39 ff2 fs3 fc0 sc0 ls0 ws0">中元素没有原象。</div><div class="t m0 x3 h6 yc1 ff2 fs3 fc0 sc0 ls0 ws0">2.<span class="_"> </span>函数:</div><div class="t m0 x3 h6 yc2 ff2 fs3 fc0 sc0 ls0 ws0">（1）<span class="_"> </span>定义：函数是由一个非空数集到时另一个非空数集的映射。</div><div class="t m0 x3 h6 yc3 ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_"> </span>函数的表示方法：列表法、<span class="sc1">图像法、解析式<span class="_ _1"></span>法</span>。</div><div class="t m0 x3 h6 yc4 ff2 fs3 fc0 sc1 ls0 ws0">注：<span class="sc0">在解函数题时可以画出图像，运用数形结合的方法可以使大部分题目变得更简单。</span></div><div class="t m0 x3 h5 yc5 ff2 fs3 fc0 sc0 ls0 ws0">3.<span class="_"> </span>函数的<span class="sc1">三要素：<span class="fs2">定义域、值域、对应法则</span></span></div><div class="t m0 x3 h6 y4c ff2 fs3 fc0 sc0 ls0 ws0">（1）</div><div class="c x4 yc6 wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x3b h6 y4c ff2 fs3 fc0 sc0 ls0 ws0">定义域的求法：使函数（的解析式）有意义的</div><div class="c xb7 yc7 w11 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xb8 h6 y4c ff2 fs3 fc0 sc0 ls0 ws0">的取值范围</div><div class="t m0 x3 h6 y4d ff2 fs3 fc0 sc0 ls0 ws0">主要依据：</div><div class="t m0 xb9 h28 yc8 ff1 fsd fc0 sc0 ls0 ws0">1</div><div class="t m0 x4 h6 y97 ff2 fs3 fc0 sc0 ls0 ws0">分母不能为<span class="_ _8a"> </span>0</div><div class="t m0 xb9 h28 yc9 ff1 fsd fc0 sc0 ls0 ws0">2</div><div class="t m0 x4 h6 yca ff2 fs3 fc0 sc0 ls0 ws0">偶次根式的被开方式</div><div class="c x22 ycb w10 h1f"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x79 h6 yca ff2 fs3 fc0 sc0 ls0 ws0">0</div><div class="t m0 xb9 h29 ycc ff6 fs3 fc0 sc0 ls0 ws0">3</div><div class="t m0 x4 h5 ycd ff2 fs2 fc0 sc1 ls0 ws0">特殊函数定义域</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89796422/bg4.jpg"><div class="c x3 y1 w2 h2"><div class="t m0 x0 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">-<span class="_ _0"> </span>4<span class="_ _0"> </span>-</div></div><div class="c x3 y56 w2d h10"><div class="t m0 x99 hc y1a ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _5"></span>,</div><div class="t m0 xba hd y19 ff1 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m0 xbb he y1a ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _27"></span><span class="_ _3f"> </span><span class="ff4">x<span class="_ _8d"></span>x<span class="_ _12"></span>y</span></div></div><div class="c x3 y5b w2e h10"><div class="t m0 xbc hc y1a ff4 fs6 fc0 sc0 ls0 ws0">R<span class="_ _41"></span>x<span class="_ _a"></span>a<span class="_ _20"></span>a<span class="_ _56"></span>a<span class="_ _12"></span>y</div><div class="t m0 xba hd y19 ff4 fs7 fc0 sc0 ls0 ws0">x</div><div class="t m0 x3b he y1a ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _2e"></span><span class="_ _8e"></span><span class="_ _58"></span><span class="_ _8f"> </span><span class="ff1">),<span class="_ _90"></span>1<span class="_ _91"></span>0<span class="_ _2c"></span>(<span class="_ _92"></span>,<span class="_ _6c"> </span><span class="ff2">且</span></span></div></div><div class="c x3 yce w2f h10"><div class="t m0 xbd he y57 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _3"></span>),<span class="_ _90"></span>1<span class="_ _91"></span>0<span class="_ _2c"></span>(<span class="_ _92"></span>,<span class="_ _8b"></span>log<span class="_ _93"> </span><span class="ff3"><span class="_ _a"></span><span class="_ _8e"></span><span class="_ _94"></span><span class="_ _95"> </span><span class="ff4">x<span class="_ _96"></span>a<span class="_ _40"></span>a<span class="_ _97"></span>x<span class="_ _98"></span>y</span></span></div><div class="t m0 xbe hd y3d ff4 fs7 fc0 sc0 ls0 ws0">a</div><div class="t m0 xbf h18 y57 ff2 fs6 fc0 sc0 ls0 ws0">且</div></div><div class="c x3 ycf w30 hb"><div class="t m0 x2a hc y10 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _15"></span>(<span class="_ _92"></span>,</div><div class="t m0 x2e hc ye ff1 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 xb5 he y10 ff1 fs6 fc0 sc0 ls0 ws0">,<span class="_ _5c"></span>tan<span class="_ _99"> </span><span class="ff4">Z<span class="_ _41"></span>k<span class="_ _30"></span>k<span class="_ _70"></span>x<span class="_ _88"></span>x<span class="_ _7d"></span>y<span class="_ _9a"> </span><span class="ff3"><span class="_ _7f"></span><span class="_ _8b"></span><span class="_ _13"></span></span></span></div><div class="t m2 x8d h22 yf ff3 fsc fc0 sc0 ls0 ws0"></div><div class="t m2 xe h22 y10 ff3 fsc fc0 sc0 ls0 ws0"></div></div><div class="t m0 x3 h6 y63 ff2 fs3 fc0 sc0 ls0 ws0">（2）</div><div class="c x4 yd0 wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x3b h6 y63 ff2 fs3 fc0 sc0 ls0 ws0">值域的求法：</div><div class="c x12 y61 wa h1a"><div class="t m0 x61 hc y62 ff4 fs6 fc0 sc0 ls0 ws0">y</div></div><div class="t m0 x48 h6 y63 ff2 fs3 fc0 sc0 ls0 ws0">的取值范围</div><div class="t m0 xb9 h6 y65 ff2 fsd fc0 sc0 ls0 ws0">1<span class="_ _9b"> </span><span class="fs3">正比例函数：</span></div><div class="c xc0 y64 w31 h1b"><div class="t m0 x7a he y32 ff4 fs6 fc0 sc0 ls0 ws0">kx<span class="_ _2c"></span>y<span class="_ _7c"> </span><span class="ff3"></span></div></div><div class="t m0 x48 h6 y65 ff2 fs3 fc0 sc0 ls0 ws0">和<span class="_"> </span>一次函数：</div><div class="c xc1 y64 w32 h1b"><div class="t m0 xb5 he y32 ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _48"></span>kx<span class="_ _18"></span>y<span class="_ _9c"> </span><span class="ff3"><span class="_ _5"></span></span></div></div><div class="t m0 x3f h6 y65 ff2 fs3 fc0 sc0 ls0 ws0">的值域为</div><div class="c xc2 yd1 we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">R</div></div><div class="t m0 xb9 h6 yd2 ff2 fsd fc0 sc0 ls0 ws0">2<span class="_ _9b"> </span><span class="fs3">二次函数：</span></div><div class="c x3c yd3 w33 h10"><div class="t m0 xe he y1a ff4 fs6 fc0 sc0 ls0 ws0">c<span class="_ _48"></span>bx<span class="_ _5f"></span>ax<span class="_ _34"></span>y<span class="_ _9d"> </span><span class="ff3"><span class="_ _2c"></span><span class="_ _b"></span></span></div><div class="t m0 xc3 hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2</div></div><div class="t m0 xc4 h6 yd2 ff2 fs3 fc0 sc0 ls0 ws0">的值域求法：配方法。如果</div><div class="c xc5 yd4 w10 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xc6 h6 yd2 ff2 fs3 fc0 sc0 ls0 ws0">的取值范围不是</div><div class="c x52 yd5 we h1a"><div class="t m0 x2f hc y30 ff4 fs6 fc0 sc0 ls0 ws0">R</div></div><div class="t m0 xc7 h6 yd2 ff2 fs3 fc0 sc0 ls0 ws0">则还需画图</div><div class="t m0 x45 h6 y15 ff2 fs3 fc0 sc0 ls0 ws0">像</div><div class="t m0 xb9 h6 yd6 ff2 fsd fc0 sc0 ls0 ws0">3<span class="_ _9b"> </span><span class="fs3">反比例函数：</span></div><div class="c xc0 yd7 w2b hb"><div class="t m0 xc8 hc ye ff4 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x61 hc y10 ff4 fs6 fc0 sc0 ls0 ws0">y</div><div class="t m0 xc9 hc yf ff1 fs6 fc0 sc0 ls0 ws0">1</div><div class="t m0 x32 he y10 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x98 h6 yd6 ff2 fs3 fc0 sc0 ls0 ws0">的值域为</div><div class="c x3e yd8 w32 h1b"><div class="t m0 xca he y32 ff1 fs6 fc0 sc0 ls0 ws0">}<span class="_ _2"></span>0<span class="_ _22"></span>|<span class="_ _47"></span>{<span class="_ _9e"> </span><span class="ff3"><span class="_ _88"></span><span class="ff4">y<span class="_ _9f"></span>y</span></span></div></div><div class="t m0 xb9 h2a yd9 ff2 fsd fc0 sc0 ls0 ws0">4</div><div class="c x45 yda w34 hb"><div class="t m0 xcb hc ye ff4 fs6 fc0 sc0 ls0 ws0">d<span class="_ _48"></span>cx</div><div class="t m0 xca hc yf ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _a0"></span>ax</div><div class="t m0 x61 hc y10 ff4 fs6 fc0 sc0 ls0 ws0">y</div><div class="t m0 xcc he ye ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xcd he yf ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x32 he y10 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xce h6 yd9 ff2 fs3 fc0 sc0 ls0 ws0">的值域为</div><div class="c x98 yda w35 hb"><div class="t m0 x3a hc y10 ff1 fs6 fc0 sc0 ls0 ws0">}<span class="_ _2e"></span>|<span class="_ _47"></span>{</div><div class="t m0 xcf hc ye ff4 fs6 fc0 sc0 ls0 ws0">c</div><div class="t m0 xcf hc yf ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 x7a he y10 ff4 fs6 fc0 sc0 ls0 ws0">y<span class="_ _9f"></span>y<span class="_ _62"> </span><span class="ff3"></span></div></div><div class="t m0 xb9 h2a y6d ff2 fsd fc0 sc0 ls0 ws0">5</div><div class="c x45 ydb w36 hb"><div class="t m0 xb9 hc ydc ff4 fs6 fc0 sc0 ls0 ws0">c<span class="_ _48"></span>bx<span class="_ _5f"></span>ax</div><div class="t m0 xd0 hc yf ff4 fs6 fc0 sc0 ls0 ws0">n<span class="_ _1c"></span>mx</div><div class="t m0 x61 hc y10 ff4 fs6 fc0 sc0 ls0 ws0">y</div><div class="t m0 xd1 he ydc ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _2c"></span></div><div class="t m0 xd2 he yf ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x32 he y10 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xcc hd ydd ff1 fs7 fc0 sc0 ls0 ws0">2</div></div><div class="t m0 x53 h6 y6d ff2 fs3 fc0 sc0 ls0 ws0">的值域求法：判别式法</div><div class="t m0 xb9 h2a yde ff2 fsd fc0 sc0 ls0 ws0">6</div><div class="t m0 x45 h6 ydf ff2 fs3 fc0 sc0 ls0 ws0">另求值域的方法：<span class="sc1">换元法</span>、反函数法、不等式法、数形结合法、函数的单调性等等。</div><div class="t m0 x3 h6 yb6 ff2 fs3 fc0 sc0 ls0 ws0">（3）<span class="_"> </span>解析式求法：</div><div class="t m0 x3 h6 ye0 ff2 fs3 fc0 sc0 ls0 ws0">在求函数解析式时可用<span class="sc1">换元法</span>、构造法、待定系数法等。</div><div class="t m0 x3 h6 ye1 ff2 fs3 fc0 sc0 ls0 ws0">4.<span class="_"> </span>函数图像的变换</div><div class="t m0 x3 h6 y79 ff2 fs3 fc0 sc0 ls0 ws0">（1）<span class="_"> </span>平移</div><div class="c x3 ye2 w37 h2b"><div class="t m0 xd3 hc ye3 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _1c"></span>(<span class="_ _a1"></span>)<span class="_ _67"></span>(<span class="_ _a2"> </span><span class="ff4">a<span class="_ _5d"></span>x<span class="_ _a3"></span>f<span class="_ _12"></span>y</span></div><div class="t m0 xd4 hc ye4 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _a4"> </span><span class="ff3"><span class="_ _96"></span><span class="_ _d"></span><span class="_ _a5"></span></span></div><div class="t m0 xd6 h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">个单位</div><div class="t m0 xca h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">向右平移</div></div><div class="c x6a ye2 w37 h2b"><div class="t m0 xd3 hc ye3 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _8b"></span>(<span class="_ _a6"></span>)<span class="_ _67"></span>(<span class="_ _a2"> </span><span class="ff4">a<span class="_ _5d"></span>x<span class="_ _a3"></span>f<span class="_ _12"></span>y</span></div><div class="t m0 xd4 hc ye4 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _a4"> </span><span class="ff3"><span class="_ _96"></span><span class="_ _d"></span><span class="_ _a5"></span></span></div><div class="t m0 xd6 h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">个单位</div><div class="t m0 xca h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">向左平移</div></div><div class="c x3 ye6 w37 h2b"><div class="t m0 xd7 hc ye3 ff4 fs6 fc0 sc0 ls0 ws0">a<span class="_ _5e"></span>x<span class="_ _53"></span>f<span class="_ _70"></span>y</div><div class="t m0 xd4 hc ye4 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _a7"> </span><span class="ff3"><span class="_ _91"></span><span class="_ _d"></span><span class="_ _a5"></span><span class="_ _a8"> </span><span class="ff1">)<span class="_ _67"></span>(<span class="_ _a6"></span>)<span class="_ _67"></span>(</span></span></div><div class="t m0 xd6 h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">个单位</div><div class="t m0 xca h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">向上平移</div></div><div class="c x6a ye6 w37 h2b"><div class="t m0 xd7 hc ye3 ff4 fs6 fc0 sc0 ls0 ws0">a<span class="_ _56"></span>x<span class="_ _53"></span>f<span class="_ _12"></span>y</div><div class="t m0 xd4 hc ye4 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _a7"> </span><span class="ff3"><span class="_ _91"></span><span class="_ _d"></span><span class="_ _a5"></span><span class="_ _a8"> </span><span class="ff1">)<span class="_ _67"></span>(<span class="_ _a6"></span>)<span class="_ _67"></span>(</span></span></div><div class="t m0 xd6 h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">个单位</div><div class="t m0 xca h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">向下平移</div></div><div class="t m0 x3 h6 ybe ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_"> </span>翻折</div><div class="c x3 ye7 w38 h2b"><div class="t m0 x7f hc ye3 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _a9"></span>)<span class="_ _67"></span>(<span class="_ _aa"> </span><span class="ff4">x<span class="_ _a3"></span>f<span class="_ _8"></span>y</span></div><div class="t m0 xb9 hc ye5 ff4 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _ab"> </span><span class="ff3"><span class="_ _53"></span><span class="_ _d"></span><span class="_ _ac"></span></span></div><div class="t m0 xbb h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">上、下对折</div><div class="t m0 xd8 h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">轴<span class="_ _2c"></span>沿</div></div><div class="c xd9 ye7 w39 h2b"><div class="t m0 x48 hc ye3 ff1 fs6 fc0 sc0 ls0 ws0">|<span class="_ _45"></span>)<span class="_ _67"></span>(<span class="_ _ad"></span>|<span class="_ _ae"></span>)<span class="_ _67"></span>(<span class="_ _af"> </span><span class="ff4">x<span class="_ _a3"></span>f<span class="_ _41"></span>y</span></div><div class="t m0 x3 hc ye5 ff4 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _b0"> </span><span class="ff3"><span class="_ _d"></span><span class="_ _b1"></span></span></div><div class="t m0 xd4 h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">下方翻折到上方</div><div class="t m0 xda h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">轴上方图像<span class="_ _b2"></span>保留</div></div><div class="c x3 ye8 w3a h2b"><div class="t m0 xdb hc ye3 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _39"></span>|<span class="_ _53"></span>|<span class="_ _39"></span>(<span class="_ _b3"></span>)<span class="_ _67"></span>(<span class="_ _b4"> </span><span class="ff4">x<span class="_ _2b"></span>f<span class="_ _12"></span>y</span></div><div class="t m0 x3 hc ye5 ff4 fs6 fc0 sc0 ls0 ws0">y</div><div class="t m0 xd5 he ye3 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _a3"></span>f<span class="_ _70"></span>y<span class="_ _b0"> </span><span class="ff3"><span class="_ _d"></span><span class="_ _b1"></span></span></div><div class="t m0 xd4 h18 ye4 ff2 fs6 fc0 sc0 ls0 ws0">右边翻折到左边</div><div class="t m0 xda h18 ye5 ff2 fs6 fc0 sc0 ls0 ws0">轴右边图像<span class="_ _b2"></span>保留</div></div><div class="t m0 x3 h6 ye9 ff2 fs3 fc0 sc0 ls0 ws0">5.<span class="_"> </span>函数的奇偶性:</div><div class="t m0 x3 h6 yea ff2 fs3 fc0 sc0 ls0 ws0">（1）<span class="_"> </span>定义域关于原点对称</div><div class="t m0 x3 h6 yeb ff2 fs3 fc0 sc0 ls0 ws0">（2）<span class="_"> </span>若</div><div class="c xa1 yec w3b h1b"><div class="t m0 x3 he y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _b"></span>)<span class="_ _3b"></span>(<span class="_ _b5"> </span><span class="ff4">x<span class="_ _a3"></span>f<span class="_ _1f"></span>x<span class="_ _26"></span>f<span class="_ _b6"> </span><span class="ff3"><span class="_ _53"></span><span class="_ _56"></span></span></span></div></div><div class="c x73 yed w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xdc h6 yeb ff2 fs3 fc0 sc0 ls0 ws0">奇<span class="_ _b7"> </span>若</div><div class="c x4f yec w3c h1b"><div class="t m0 xdd he y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _2c"></span>)<span class="_ _4a"></span>(<span class="_ _b8"> </span><span class="ff4">x<span class="_ _a3"></span>f<span class="_ _b9"></span>x<span class="_ _26"></span>f<span class="_ _ba"> </span><span class="ff3"><span class="_ _2a"></span></span></span></div></div><div class="c xde yed w18 h23"><div class="t m0 x2f he y4a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xdf h6 yeb ff2 fs3 fc0 sc0 ls0 ws0">偶</div><div class="t m0 x3 h6 y4e ff2 fs3 fc0 sc0 ls0 ws0">注：①若奇函数在</div><div class="c x85 yee w3d h21"><div class="t m0 x9c he ya1 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _88"></span><span class="ff3"><span class="_ _4"></span><span class="ff4">x</span></span></div></div><div class="t m0 x73 h6 y4e ff2 fs3 fc0 sc0 ls0 ws0">处有意义，则</div><div class="c xe0 yef w3e h1b"><div class="t m0 xcd he y32 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _5d"></span>)<span class="_ _11"></span>0<span class="_ _11"></span>(<span class="_ _bb"> </span><span class="ff3"><span class="_ _34"></span><span class="ff4">f</span></span></div></div><div class="t m0 x3 h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">②常值函数</div><div class="c x46 yf0 w1f h1b"><div class="t m0 xbe he y32 ff4 fs6 fc0 sc0 ls0 ws0">a<span class="_ _a0"></span>x<span class="_ _53"></span>f<span class="_ _bc"> </span><span class="ff3"><span class="_ _63"></span><span class="ff1">)<span class="_ _67"></span>(</span></span></div></div><div class="t m0 xe1 h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">（</div><div class="c xe2 yf1 w24 h21"><div class="t m0 x9c he ya1 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _83"></span><span class="ff3"><span class="_ _83"></span><span class="ff4">a</span></span></div></div><div class="t m0 x87 h6 y52 ff2 fs3 fc0 sc0 ls0 ws0">）为偶函数</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89796422/bg5.jpg"><div class="c x1 y1 w2 h2"><div class="t m0 x0 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">-<span class="_ _0"> </span>5<span class="_ _0"> </span>-</div></div><div class="t m0 x3 h6 yf2 ff2 fs3 fc0 sc0 ls0 ws0">③</div><div class="c xa9 yf3 w3e h1b"><div class="t m0 xbe he y32 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _5d"></span>)<span class="_ _67"></span>(<span class="_ _bd"> </span><span class="ff3"><span class="_ _9f"></span><span class="ff4">x<span class="_ _53"></span>f</span></span></div></div><div class="t m0 xa h6 yf2 ff2 fs3 fc0 sc0 ls0 ws0">既是奇函数又是偶函数</div><div class="t m0 x3 h6 yf4 ff2 fs3 fc0 sc0 ls0 ws0">6.</div><div class="c x45 yf5 wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xe3 h6 yf4 ff2 fs3 fc0 sc0 ls0 ws0">函数的单调性:</div><div class="t m0 x3 h6 yf6 ff2 fs3 fc0 sc0 ls0 ws0">对于</div><div class="c x2e yf7 w3f h24"><div class="t m0 xe hc y50 ff1 fs6 fc0 sc0 ls0 ws0">]<span class="_ _be"></span>,<span class="_ _63"></span>[</div><div class="t m0 xcc hd yf8 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _70"></span>1</div><div class="t m0 xe4 he y50 ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _53"></span>a<span class="_ _8b"></span>x<span class="_ _41"></span>x<span class="_ _ba"> </span><span class="ff3"><span class="_ _bf"></span><span class="_ _c0"> </span><span class="ff2">、</span></span></div></div><div class="t m0 xe5 h6 yf6 ff2 fs3 fc0 sc0 ls0 ws0">且</div><div class="c x9 yf7 w40 h24"><div class="t m0 xe6 hd yf8 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _56"></span>1</div><div class="t m0 x5c he y50 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _48"></span>x<span class="_ _c1"> </span><span class="ff3"></span></div></div><div class="t m0 x81 h6 yf6 ff2 fs3 fc0 sc0 ls0 ws0">，若</div><div class="c x3 yf9 w41 h2c"><div class="t m0 x2f he yfa ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he yfb ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he yfc ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xbe he yfd ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xbe he yfe ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x47 h18 yfd ff2 fs6 fc0 sc0 ls0 ws0">上为减函数<span class="_ _79"></span>在<span class="_ _c2"></span>称</div><div class="t m0 x47 h18 yfe ff2 fs6 fc0 sc0 ls0 ws0">上为增函数<span class="_ _79"></span>在<span class="_ _c2"></span>称</div><div class="t m0 x29 hc yfd ff1 fs6 fc0 sc0 ls0 ws0">]<span class="_ _be"></span>,<span class="_ _63"></span>[<span class="_ _55"></span>)<span class="_ _67"></span>(<span class="_ _22"></span>),<span class="_ _5d"></span>(<span class="_ _2c"></span>)<span class="_ _55"></span>(</div><div class="t m0 x29 hc yfe ff1 fs6 fc0 sc0 ls0 ws0">]<span class="_ _be"></span>,<span class="_ _63"></span>[<span class="_ _55"></span>)<span class="_ _67"></span>(<span class="_ _22"></span>),<span class="_ _5d"></span>(<span class="_ _2c"></span>)<span class="_ _55"></span>(</div><div class="t m0 xe4 hd yff ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _37"></span>1</div><div class="t m0 xe4 hd y100 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _59"></span>1</div><div class="t m0 xa0 hc yfd ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _53"></span>a<span class="_ _8"></span>x<span class="_ _a3"></span>f<span class="_ _4d"></span>x<span class="_ _a3"></span>f<span class="_ _1c"></span>x<span class="_ _a3"></span>f</div><div class="t m0 xa0 hc yfe ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _53"></span>a<span class="_ _8"></span>x<span class="_ _a3"></span>f<span class="_ _4d"></span>x<span class="_ _a3"></span>f<span class="_ _1c"></span>x<span class="_ _53"></span>f</div></div><div class="t m0 x3 h6 y101 ff2 fs3 fc0 sc0 ls0 ws0">增函数：</div><div class="c xa1 y102 w10 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xbc h6 y101 ff2 fs3 fc0 sc0 ls0 ws0">值越大，函数值越大；</div><div class="c xe7 y102 w11 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 x2d h6 y101 ff2 fs3 fc0 sc0 ls0 ws0">值越小，函数值越小。</div><div class="t m0 x3 h6 y103 ff2 fs3 fc0 sc0 ls0 ws0">减函数：</div><div class="c xa1 y104 w10 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xbc h6 y103 ff2 fs3 fc0 sc0 ls0 ws0">值越大，函数值反而越小；</div><div class="c xe8 y104 w11 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xe9 h6 y103 ff2 fs3 fc0 sc0 ls0 ws0">值越小，函数值反而越大。</div><div class="t m0 x3 h6 y65 ff2 fs3 fc0 sc0 ls0 ws0">复合函数的单调性：</div><div class="c x86 y64 w3b h1b"><div class="t m0 xe4 he y32 ff1 fs6 fc0 sc0 ls0 ws0">))<span class="_ _55"></span>(<span class="_ _83"></span>(<span class="_ _2c"></span>)<span class="_ _be"></span>(<span class="_ _c3"> </span><span class="ff4">x<span class="_ _c4"></span>g<span class="_ _c4"></span>f<span class="_ _48"></span>x<span class="_ _53"></span>h<span class="_ _10"> </span><span class="ff3"></span></span></div></div><div class="c x3 y66 w42 h1b"><div class="t m0 x9c hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _a3"></span>f</span></div></div><div class="t m0 x33 h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">与</div><div class="c x26 y66 w15 h1b"><div class="t m0 xea hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _ad"></span>g</span></div></div><div class="t m0 xab h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">同增或同减时复合函数</div><div class="c xeb y66 w43 h1b"><div class="t m0 xec hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _53"></span>h</span></div></div><div class="t m0 x64 h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">为增函数；</div><div class="c xed y66 w42 h1b"><div class="t m0 x9c hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _a3"></span>f</span></div></div><div class="t m0 xaf h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">与</div><div class="c x2c y66 w44 h1b"><div class="t m0 xea hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _c4"></span>g</span></div></div><div class="t m0 xee h6 y67 ff2 fs3 fc0 sc0 ls0 ws0">相异时<span class="_ _c6"></span>（一增一减）<span class="_ _c6"></span>复合函</div><div class="t m0 x3 h6 y105 ff2 fs3 fc0 sc0 ls0 ws0">数</div><div class="c xa9 y106 w28 h1b"><div class="t m0 xec hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _a3"></span>h</span></div></div><div class="t m0 xf h6 y105 ff2 fs3 fc0 sc0 ls0 ws0">为减函数。</div><div class="t m0 x3 h6 y68 ff2 fs3 fc0 sc0 ls0 ws0">注：奇偶性和单调性同时出现时可用画图的方法判断。</div><div class="t m0 x3 h6 y69 ff2 fs3 fc0 sc0 ls0 ws0">7.<span class="_"> </span>二次函数:</div><div class="t m0 x3 h6 y6b ff2 fs3 fc0 sc0 ls0 ws0">（1）二次函数的三种解析式:</div><div class="t m0 x3 h6 y107 ff2 fs3 fc0 sc0 ls0 ws0">①一般式：</div><div class="c x46 y108 w45 h10"><div class="t m0 x45 he y1a ff4 fs6 fc0 sc0 ls0 ws0">c<span class="_ _48"></span>bx<span class="_ _5f"></span>ax<span class="_ _4b"></span>x<span class="_ _a3"></span>f<span class="_ _c7"> </span><span class="ff3"><span class="_ _2c"></span><span class="_ _b"></span></span></div><div class="t m0 xef hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9c hc y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(</div></div><div class="t m0 x88 h6 y107 ff2 fs3 fc0 sc0 ls0 ws0">（</div><div class="c x97 y109 w24 h19"><div class="t m0 x9c he y2e ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _83"></span><span class="ff3"><span class="_ _83"></span><span class="ff4">a</span></span></div></div><div class="t m0 x63 h6 y107 ff2 fs3 fc0 sc0 ls0 ws0">）</div><div class="t m0 x3 h6 y10a ff2 fs3 fc0 sc0 ls0 ws0">②</div><div class="c xa9 y10b wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x8d h6 y10a ff2 fs3 fc0 sc0 ls0 ws0">顶点式：</div><div class="c x31 y10c w46 h10"><div class="t m0 x8d he y1a ff4 fs6 fc0 sc0 ls0 ws0">h<span class="_ _c8"></span>k<span class="_ _3c"></span>x<span class="_ _a3"></span>a<span class="_ _48"></span>x<span class="_ _a3"></span>f<span class="_ _c9"> </span><span class="ff3"><span class="_ _4d"></span><span class="_ _29"></span></span></div><div class="t m0 x65 hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2</div><div class="t m0 xf0 hc y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _1c"></span>(<span class="_ _5e"></span>)<span class="_ _67"></span>(</div></div><div class="t m0 xeb h6 y10a ff2 fs3 fc0 sc0 ls0 ws0">（</div><div class="c xf1 y10d w26 h19"><div class="t m0 x9c he y2e ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _83"></span><span class="ff3"><span class="_ _83"></span><span class="ff4">a</span></span></div></div><div class="t m0 xf2 h6 y10a ff2 fs3 fc0 sc0 ls0 ws0">）<span class="_ _39"></span>，其中</div><div class="c xed y10c w24 h1b"><div class="t m0 xc9 hc y32 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>,<span class="_ _63"></span>(<span class="_ _ca"> </span><span class="ff4">h<span class="_ _47"></span>k</span></div></div><div class="t m0 xb8 h6 y10a ff2 fs3 fc0 sc0 ls0 ws0">为顶点</div><div class="t m0 x3 h6 y77 ff2 fs3 fc0 sc0 ls0 ws0">③两根式：</div><div class="c x46 y10e w25 h24"><div class="t m0 x23 hc y50 ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _7d"></span>)(<span class="_ _5f"></span>(<span class="_ _5e"></span>)<span class="_ _be"></span>(</div><div class="t m0 xf hd yf8 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _5f"></span>1</div><div class="t m0 xf3 he y50 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _5d"></span>x<span class="_ _70"></span>x<span class="_ _5d"></span>x<span class="_ _47"></span>a<span class="_ _48"></span>x<span class="_ _a3"></span>f<span class="_ _cb"> </span><span class="ff3"><span class="_ _40"></span><span class="_ _15"></span></span></div></div><div class="t m0 xf1 h6 y77 ff2 fs3 fc0 sc0 ls0 ws0">（</div><div class="c x9f y10f w26 h21"><div class="t m0 x9c he ya1 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _83"></span><span class="ff3"><span class="_ _83"></span><span class="ff4">a</span></span></div></div><div class="t m0 x94 h6 y77 ff2 fs3 fc0 sc0 ls0 ws0">）<span class="_ _39"></span>，其中</div><div class="c xf4 y10e w47 h24"><div class="t m0 x93 hd yf8 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _70"></span>1</div><div class="t m0 x7a h18 y50 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _41"></span>x<span class="_ _66"> </span><span class="ff2">、</span></div></div><div class="t m0 xdf h6 y77 ff2 fs3 fc0 sc0 ls0 ws0">是</div><div class="c xf5 y78 w3e h1b"><div class="t m0 xbe he y32 ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _5d"></span>)<span class="_ _67"></span>(<span class="_ _bd"> </span><span class="ff3"><span class="_ _9f"></span><span class="ff4">x<span class="_ _53"></span>f</span></span></div></div><div class="t m0 xf6 h6 y77 ff2 fs3 fc0 sc0 ls0 ws0">的两根</div><div class="t m0 x3 h6 y79 ff2 fs3 fc0 sc0 ls0 ws0">（2）图像与性质:</div><div class="c x3 y110 wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x9d h6 y21 ff2 fs3 fc0 sc0 ls0 ws0">二次函数的图像是一条抛物线，有如下特征与性质：</div><div class="t m0 xb9 h2a y111 ff2 fsd fc0 sc0 ls0 ws0">1</div><div class="t m0 x45 h6 y112 ff2 fs3 fc0 sc0 ls0 ws0">开口</div><div class="c x46 y113 w48 h21"><div class="t m0 xac he ya1 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _36"></span><span class="_ _8a"> </span><span class="ff1">0<span class="_ _54"></span><span class="ff4">a</span></span></div></div><div class="t m0 xf7 h6 y112 ff2 fs3 fc0 sc0 ls0 ws0">开口向上</div><div class="c xf8 y113 w49 h21"><div class="t m0 xac he ya1 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _36"></span><span class="_ _8a"> </span><span class="ff1">0<span class="_ _12"></span><span class="ff4">a</span></span></div></div><div class="t m0 xf9 h6 y112 ff2 fs3 fc0 sc0 ls0 ws0">开口向下</div><div class="t m0 xb9 h2a y114 ff2 fsd fc0 sc0 ls0 ws0">2</div><div class="c x45 y115 wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xe3 h6 y114 ff2 fs3 fc0 sc0 ls0 ws0">对称轴：</div><div class="c x47 y116 w3e hb"><div class="t m0 xcd hc ye ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xfa hc yf ff4 fs6 fc0 sc0 ls0 ws0">b</div><div class="t m0 x2f hc y10 ff4 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 xac hc ye ff1 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9c he y10 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _53"></span></div></div><div class="t m0 xb9 h2a y117 ff2 fsd fc0 sc0 ls0 ws0">3</div><div class="c x45 y118 wa h1a"><div class="t m0 x2f he y30 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xe3 h6 y117 ff2 fs3 fc0 sc0 ls0 ws0">顶点坐标：</div><div class="c xfb y119 w36 h2b"><div class="t m0 x65 hc y11a ff1 fs6 fc0 sc0 ls0 ws0">)</div><div class="t m0 xd4 hc y11b ff1 fs6 fc0 sc0 ls0 ws0">4</div><div class="t m0 xd5 hc y11c ff1 fs6 fc0 sc0 ls0 ws0">4</div><div class="t m0 xac hc y11a ff1 fs6 fc0 sc0 ls0 ws0">,</div><div class="t m0 x90 hc y11b ff1 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 x2f hc y11a ff1 fs6 fc0 sc0 ls0 ws0">(</div><div class="t m0 x3 hd y11d ff1 fs7 fc0 sc0 ls0 ws0">2</div><div class="t m0 xd6 hc y11b ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xfc hc y11c ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _a0"></span>ac</div><div class="t m0 x7a hc y11b ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xec he y11c ff4 fs6 fc0 sc0 ls0 ws0">b<span class="_ _cc"> </span><span class="ff3"></span></div><div class="t m0 xfd he y11a ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xb9 h2a y11e ff2 fsd fc0 sc0 ls0 ws0">4</div><div class="c x45 y11f wa h12"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="t m0 xe3 h6 y120 ff2 fs3 fc0 sc0 ls0 ws0">与</div><div class="c xaa y121 w11 h23"><div class="t m0 x2f hc y4a ff4 fs6 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xfe h6 y120 ff2 fs3 fc0 sc0 ls0 ws0">轴的交点：</div><div class="c x54 y122 w1c h2d"><div class="t m0 x2f he y123 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y124 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y125 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y126 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y127 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xff he y128 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _36"></span><span class="_ _c4"></span></div><div class="t m0 xcf he y129 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _36"></span><span class="_ _ad"></span></div><div class="t m0 xcd he y12a ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _36"></span><span class="_ _ad"></span></div><div class="t m0 x100 h18 y128 ff2 fs6 fc0 sc0 ls0 ws0">无交点</div><div class="t m0 x3 h18 y129 ff2 fs6 fc0 sc0 ls0 ws0">交点<span class="_ _cd"></span>有</div><div class="t m0 xd2 h18 y12a ff2 fs6 fc0 sc0 ls0 ws0">有两交点</div><div class="t m0 xc3 hc y128 ff1 fs6 fc0 sc0 ls0 ws0">0</div><div class="t m0 xe4 hc y129 ff1 fs6 fc0 sc0 ls0 ws0">1<span class="_ _5f"></span>0</div><div class="t m0 xba hc y12a ff1 fs6 fc0 sc0 ls0 ws0">0</div></div><div class="t m0 xb9 h2a y12b ff2 fsd fc0 sc0 ls0 ws0">5</div><div class="t m0 x45 h6 yc3 ff2 fs3 fc0 sc0 ls0 ws0">一元二次方程根与系数的关系：<span class="_ _39"></span>（韦达定理）</div><div class="c x3 y12c wa h12"><div class="t m0 x2f he y24 ff3 fs6 fc0 sc0 ls0 ws0"></div></div><div class="c x8c y12d w4a h2e"><div class="t m0 x2f he y12e ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y12f ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y130 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y131 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he y132 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xca he y133 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _c"></span></div><div class="t m0 x101 he y134 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _53"></span><span class="_ _36"></span></div><div class="t m0 x99 hc y135 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 x99 hc y136 ff4 fs6 fc0 sc0 ls0 ws0">c</div><div class="t m0 x27 hc y133 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _3c"></span>x</div><div class="t m0 xdd hc y137 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xdd hc y138 ff4 fs6 fc0 sc0 ls0 ws0">b</div><div class="t m0 x102 hc y134 ff4 fs6 fc0 sc0 ls0 ws0">x<span class="_ _56"></span>x</div><div class="t m0 xbe hd y139 ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _4a"></span>1</div><div class="t m0 xcc hd y13a ff1 fs7 fc0 sc0 ls0 ws0">2<span class="_ _5c"></span>1</div></div><div class="t m0 xb9 h2a y13b ff2 fsd fc0 sc0 ls0 ws0">6</div><div class="c x45 y13c w45 h10"><div class="t m0 x45 he y1a ff4 fs6 fc0 sc0 ls0 ws0">c<span class="_ _48"></span>bx<span class="_ _5f"></span>ax<span class="_ _4b"></span>x<span class="_ _a3"></span>f<span class="_ _c7"> </span><span class="ff3"><span class="_ _2c"></span><span class="_ _b"></span></span></div><div class="t m0 xef hd y19 ff1 fs7 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9c hc y1a ff1 fs6 fc0 sc0 ls0 ws0">)<span class="_ _67"></span>(</div></div><div class="t m0 x95 h6 y13b ff2 fs3 fc0 sc0 ls0 ws0">为偶函数的充要条件为</div><div class="c xf8 y13d w4b h19"><div class="t m0 xea he y2e ff1 fs6 fc0 sc0 ls0 ws0">0<span class="_ _88"></span><span class="ff3"><span class="_ _83"></span><span class="ff4">b</span></span></div></div><div class="t m0 xb9 h2a yc9 ff2 fsd fc0 sc0 ls0 ws0">7</div><div class="t m0 x45 h6 yca ff2 fs3 fc0 sc0 ls0 ws0">二次函数（二次函数恒大（小）于<span class="_ _8a"> </span>0）</div><div class="c x3 y13e w4c h2f"><div class="t m0 x103 he y1a ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _8"></span><span class="_ _8a"> </span><span class="ff1">0<span class="_ _5d"></span>)<span class="_ _67"></span>(<span class="_ _c5"></span><span class="ff4">x<span class="_ _a3"></span>f</span></span></div></div><div class="c x2b y13f w4d h27"><div class="t m0 x2f he yb1 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he yb2 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x2f he yb3 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xcd he y140 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 xec he yb4 ff3 fs6 fc0 sc0 ls0 ws0"><span class="_ _c4"></span></div><div class="t m0 x6b he yb5 ff3 fs6 fc0 sc0 ls0 ws0"></div><div class="t m0 x104 h18 y140 ff2 fs6 fc0 sc0 ls0 ws0">轴上方<span class="_ _b2"></span>图像位于<span class="ff4">x</span></div><div class="t m0 x56 hc yb5 ff4 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 x93 hc yb4 ff1 fs6 fc0 sc0 ls0 ws0">0</div><div class="t m0 x93 hc yb5 ff1 fs6 fc0 sc0 ls0 ws0">0</div></div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div>