函數(shù)的四個(gè)性質(zhì)

1、第1頁(yè)函數(shù)的性質(zhì)函數(shù)的性質(zhì)(奇偶性，單調(diào)性，周期性，對(duì)稱性奇偶性，單調(diào)性，周期性，對(duì)稱性)定義域優(yōu)先定義域優(yōu)先一、奇偶性常用性質(zhì)一、奇偶性常用性質(zhì)：1是既奇又偶函數(shù)；0)(?xf2奇函數(shù)若在處有定義，則必有；0?x0)0(?f3偶函數(shù)滿足；)()()(xfxfxf???4奇函數(shù)圖象關(guān)于原點(diǎn)對(duì)稱，偶函數(shù)圖象關(guān)于y軸對(duì)稱；5除外的所有函數(shù)奇偶性滿足：0)(?xf奇函數(shù)奇函數(shù)=奇函數(shù)奇函數(shù)奇函數(shù)=偶函數(shù)奇函數(shù)偶函數(shù)=非奇非偶奇函數(shù)偶函數(shù)=奇函

2、數(shù)偶函數(shù)偶函數(shù)=偶函數(shù)偶函數(shù)偶函數(shù)=偶函數(shù)6任何函數(shù)可以寫(xiě)成一個(gè)奇函數(shù)和一個(gè)偶函數(shù))(xf2)()()(xfxfx????的和。2)()()(xfxfx????二、二、函數(shù)函數(shù)圖象本身的對(duì)稱性（自身對(duì)稱）圖象本身的對(duì)稱性（自身對(duì)稱）)(xfy?若，則具有周期性；若，則()()fxafxb????()fx()()faxfbx????具有對(duì)稱性：“內(nèi)同表示周期性，內(nèi)反表示對(duì)稱性內(nèi)同表示周期性，內(nèi)反表示對(duì)稱性”。()fx1、圖象關(guān)于直線圖象關(guān)

3、于直線對(duì)稱對(duì)稱)()(xbfxaf????)(xfy?22)()(baxbxax??????推論推論1：的圖象關(guān)于直線的圖象關(guān)于直線對(duì)稱對(duì)稱)()(xafxaf????)(xfy?ax?推論推論2、的圖象關(guān)于直線的圖象關(guān)于直線對(duì)稱對(duì)稱)2()(xafxf???)(xfy?ax?推論推論3、的圖象關(guān)于直線的圖象關(guān)于直線對(duì)稱對(duì)稱)2()(xafxf????)(xfy?ax?2、的圖象關(guān)于點(diǎn)的圖象關(guān)于點(diǎn)對(duì)稱對(duì)稱cxbfxaf2)()(????

4、?)(xfy?)2(cba?推論1、的圖象關(guān)于點(diǎn)對(duì)稱bxafxaf2)()(?????)(xfy?)(ba推論2、的圖象關(guān)于點(diǎn)對(duì)稱bxafxf2)2()(????)(xfy?)(ba推論3、的圖象關(guān)于點(diǎn)對(duì)稱bxafxf2)2()(?????)(xfy?)(ba三、函數(shù)周期性的幾個(gè)重要結(jié)論函數(shù)周期性的幾個(gè)重要結(jié)論1、()的周期為，()也是函數(shù)的周期()()fxTfx??0T??)(xfy?TkTkZ?第3頁(yè)4、已知，那么112)(???x

5、xxf???????????)8()6()4()2()0()2()4()6(ffffffffA.14B.15C.D.1616?5、已知的定義域?yàn)镽，若都為奇函數(shù)，則)(xf)1()1(??xfxf、A.為偶函數(shù)B.為奇函數(shù)C.=D.為奇函數(shù))(xf)(xf)(xf)2(?xf)3(?xf6、定義在R上的函數(shù)對(duì)任意的實(shí)數(shù)都有，則下列結(jié)論一)(xfx)1()1(????xfxf定成立的是A.的周期為4B.的周期為6)(xf)(xfC.的圖像

6、關(guān)于直線對(duì)稱D.的圖像關(guān)于點(diǎn)(10)對(duì)稱)(xf1?x)(xf7、定義在R上的函數(shù)滿足:，當(dāng)[1])(xf)()(xfxf???)1()1(xfxf????x1?時(shí)，，則3)(xxf??)2013(fA.B.0C.1D.21?8、定義在R上的函數(shù)對(duì)任意的實(shí)數(shù)都有，并且為)(xfx)2()2(xfxf???)1(?xf偶函數(shù).若，那么3)1(?f?)101(fA.1B.2C.3D.49、已知f(x)(x∈R)為奇函數(shù)，f(2)＝1，f(x

7、＋2)＝f(x)＋f(2)，則f(3)等于()A.B1C.D2123210、若奇函數(shù)f(x)(x∈R)滿足f(3)＝1，f(x＋3)＝f(x)＋f(3)，則f等于()(32)A0B1C.D－121211、已知定義在R上的奇函數(shù)f(x)滿足f(x－4)＝－f(x)，且在區(qū)間[02]上是增函數(shù)，則()Af(－25)f(11)f(80)Bf(80)f(11)f(－25)Cf(11)f(80)f(－25)Df(－25)f(80)f(11)12、