第7天屠龍后——函數(shù)的奇偶江湖兵刃重器之倚天名稱：倚天材料：玄鐵，精內(nèi)藏降龍十八掌掌法精江湖兵刃重器之屠龍名稱：屠龍材料：玄鐵，精內(nèi)藏倚天劍與屠龍倚天屠一刀一劍，一陰一陽(yáng)相互對(duì)立，相互依存2.6函數(shù)的奇偶筆2.6函數(shù)的奇偶函數(shù)的自身代數(shù)性奇函偶函筆2.6函數(shù)的奇偶1.函數(shù)自身代數(shù)性質(zhì)：奇函數(shù)、偶函筆2.6函數(shù)的奇偶1.函數(shù)自身代數(shù)性質(zhì)：奇函數(shù)、偶函2.定義筆2.6函數(shù)的奇偶1.函數(shù)自身代數(shù)性質(zhì)：奇函數(shù)、偶函2.定義既奇又偶函非奇非偶函筆2.6函數(shù)的奇偶1.函數(shù)自身代數(shù)性質(zhì)：奇函數(shù)、偶函2.定義奇函數(shù)

f(x f(x)f(x f(x)既奇又偶函數(shù)：同時(shí)滿足奇偶函數(shù)條非奇非偶函數(shù)：同時(shí)不滿足奇偶函數(shù)條f(x) f(x)=3x 4x3定義法判定奇偶函一般步1、判定定義域是否關(guān)于原點(diǎn)對(duì)2、判斷f(-x)是否等于f(x)或者-f(x)=x4 3x2f(x)=x2 x211f(x)=x211筆2.6函數(shù)的奇偶3.定義判斷函數(shù)奇偶判斷定義域是否關(guān)于原點(diǎn)對(duì)f(x) x3,x[2,f(x) x3,x[2,11xx判斷函數(shù)奇11xxf(x) (x1)1判斷函數(shù)奇偶1f(x)| 3| x2 2|x|1的奇偶2x3,x2x3,x02x00判斷f(x) x筆2.6函數(shù)的奇偶4.圖像性 x2筆2.6函數(shù)的奇偶4.圖像性奇函數(shù)：關(guān)于原點(diǎn)中心對(duì)偶函數(shù)：關(guān)于y軸對(duì)奇偶函數(shù)性質(zhì)對(duì)奇函偶函練習(xí)：若f(x)是奇函數(shù)，其圖像關(guān)于 x對(duì)練習(xí)：若f(x)是奇函數(shù)，點(diǎn)(af(a))在圖像則下列哪個(gè)點(diǎn)一定在圖像上（A.(a,f(a)) fC.(a,fD.(a, f練習(xí)：若f(x)是奇函數(shù)，當(dāng)x0f(x) 2x 3,則f(2) 144圖像法法判定奇偶函奇函數(shù)：圖象關(guān)于原點(diǎn)對(duì)偶函數(shù)：圖象關(guān)于y軸對(duì)筆2.6函數(shù)的奇偶5.圖像法判斷奇偶奇函數(shù)：圖象關(guān)于原點(diǎn)對(duì)偶函數(shù)：圖象關(guān)于y軸對(duì)筆二、函2.6函數(shù)的奇偶6.性質(zhì)奇函數(shù)只有奇數(shù)次，偶函數(shù)只有偶數(shù)奇函數(shù)并且f(x)在x=0處有定義，則奇偶函數(shù)的性2.奇偶函數(shù)的和、差、筆2.6函數(shù)的奇偶6.性質(zhì)奇偶偶偶奇偶函數(shù)的性奇偶函數(shù)的單調(diào)奇函數(shù)在[ab]和[b,a上有相同的單調(diào)性偶函數(shù)在[ab]和[b,a上有相反的單調(diào)筆2.6函數(shù)的奇偶6.性質(zhì)(3)[ab]上f(x)單調(diào)遞增(遞減f(x)奇函數(shù) f(x)[b,a]遞增(遞減f(x)偶函數(shù) f(x)[b,a]遞減(遞增偶函數(shù)在對(duì)稱區(qū)間單調(diào)性相偶函數(shù)f(x)[ab]是減函數(shù)，則f(x)[b,a練習(xí)：如果奇函數(shù)f(x)在(0,)是增函數(shù)則f(x)在(,0)是 練習(xí)：奇函數(shù)f(x)在區(qū)間[2,1]上有最大值最小值3，則f(x)[1,2]最大值5，最小值最小值5，最大值-最小值5，最大值練習(xí)：若f(x)[5,5]是奇函數(shù)，且f(3) A.ff(3)A.fB.f ff ff(3) f練習(xí)：若f(x)是偶函數(shù)，且在(,1)單調(diào)遞減有最小值為3，則f(x)在(1, 單調(diào)遞減有最小值單調(diào)遞增有最大值3函數(shù)對(duì)稱性關(guān)于原點(diǎn)對(duì)稱(x,y) (-x,-(x, (x,-(x, (x, (x, x, (x, (x, (x, x, 函數(shù)對(duì)稱性關(guān)于原點(diǎn)對(duì)稱：f(x) f(-x)關(guān)于x軸對(duì)稱：f(x) f(x)關(guān)于y軸對(duì)稱：f(x) f(x) a對(duì)稱：f(x) f b對(duì)稱：f(x) f(x)關(guān)于某點(diǎn)（a,b）對(duì)稱：f(x) f 已知f(x) 5,f(3) 5,則f 第二章小

第二章小映射

函數(shù)

表示方

函數(shù)

圖像

單調(diào)增函

奇偶奇函解析

減函

偶函已知f(x)是偶函數(shù)，g(x)f(x) g(x) x2 2,求f(x),g(x) 1的函數(shù)已知f(x) ,8已知二次函數(shù)f(x) c(xR)，當(dāng)x 武林多變，入行謹(jǐn)慎命 現(xiàn)實(shí)生活中，我 運(yùn)該去向何方呢命運(yùn)EveryonewasbornYoucannotchoosewhoyouButyoucandeci