函數(shù)奇偶性、對(duì)稱(chēng)性與周期性有關(guān)結(jié)論

1、函數(shù)奇偶性、對(duì)稱(chēng)性與周期性函數(shù)奇偶性、對(duì)稱(chēng)性與周期性奇偶性、對(duì)稱(chēng)性和周期性是函數(shù)的重要性質(zhì)，下面總結(jié)關(guān)于它們的一些重要結(jié)論及運(yùn)用它們解決抽象型函數(shù)的有關(guān)習(xí)題。一、幾個(gè)重要的結(jié)論（一）函數(shù)圖象本身的對(duì)稱(chēng)性（自身對(duì)稱(chēng)）)(xfy?2、的圖象關(guān)于直線(xiàn)對(duì)稱(chēng)。)2()(xafxf???)(xfy?ax?3、的圖象關(guān)于直線(xiàn)對(duì)稱(chēng)。)2()(xafxf????)(xfy?ax?4、的圖象關(guān)于直線(xiàn)對(duì)稱(chēng)。)()(xbfxaf????)(xfy?22)()(

2、baxbxax??????5、的圖象關(guān)于點(diǎn)對(duì)稱(chēng)。bxafxaf2)()(?????)(xfy?)(ba6、的圖象關(guān)于點(diǎn)對(duì)稱(chēng)。bxafxf2)2()(????)(xfy?)(ba7、的圖象關(guān)于點(diǎn)對(duì)稱(chēng)。bxafxf2)2()(?????)(xfy?)(ba8、的圖象關(guān)于點(diǎn)對(duì)稱(chēng)。cxbfxaf2)()(?????)(xfy?)2(cba?（二）兩個(gè)函數(shù)的圖象對(duì)稱(chēng)性（相互對(duì)稱(chēng)）（利用解析幾何中的對(duì)稱(chēng)曲線(xiàn)軌跡方程理解）1、函數(shù)與圖象關(guān)于直線(xiàn)對(duì)稱(chēng)。

3、)(xafy??)(xafy??0?x2、函數(shù)與圖象關(guān)于直線(xiàn)對(duì)稱(chēng))(xfy?)2(xafy??ax?3、函數(shù)與圖象關(guān)于直線(xiàn)對(duì)稱(chēng))(xfy??)2(xafy??ax??4、函數(shù)與圖象關(guān)于直線(xiàn)對(duì)稱(chēng))(xafy??)(xbfy??0)()(????xbxa即直線(xiàn)對(duì)稱(chēng)2abx??5、函數(shù)與圖象關(guān)于X軸對(duì)稱(chēng)。)(xfy?)(xfy??6、函數(shù)與圖象關(guān)于Y軸對(duì)稱(chēng)。)(xfy?)(xfy??二、例題講授例題1（1）已知是定義在實(shí)數(shù)集R上奇函數(shù)，時(shí)，，

4、求)(xfy?0?x12)(??xxf的解析式。)(xfy?（2）已知滿(mǎn)足，時(shí)，，求的)(xfy?)1()1(xfxf???1?x12)(??xxf)(xfy?解析式。（3）已知奇函數(shù)滿(mǎn)足，時(shí)，，求)(xfy?)1()1(xfxf???02???x12)(??xxf)18(log2f（4）已知滿(mǎn)足，時(shí)，，求)(xfy?0)1()1(????xfxf1?x12)(??xxf的解析式。)(xfy?例題2（1）已知，求2sin)(???xba

5、xxf1)2(?f)2(?f（2）已知偶函數(shù))(xfy?定義域?yàn)镽，且恒滿(mǎn)足)2()2(xfxf???，若方程0)(?xf在??40上只有三個(gè)實(shí)根，且一個(gè)根是4，求方程在區(qū)間??108?中的根（3）已知，求的值122)(??xxxf)6()5()4()5(ffff???????例題3（１）設(shè)函數(shù))(xfy?的定義域?yàn)镽，若的圖象關(guān)于對(duì)稱(chēng)，則函數(shù)滿(mǎn)足)(xfy?1?xA、B、)1()(xfxf??0)2()(???xfxfC、D、)1()