1.偶函數(shù)
一般地,設(shè)函數(shù)y=f(x)的定義域為A,如果對于任意的x∈A,都有f(-x)=f(x),那么稱函數(shù)y=f(x)是偶函數(shù).
2.奇函數(shù)
一般地,設(shè)函數(shù)y=f(x)的定義域為A,如果對于任意的x∈A,都有f(-x)=-f(x),那么稱函數(shù)y=f(x)是奇函數(shù).
3.奇偶性
如果函數(shù)f(x)是奇函數(shù)或偶函數(shù),我們就說函數(shù)f(x)具有奇偶性.
4.奇、偶函數(shù)的圖象性質(zhì)
(1)偶函數(shù)的圖象關(guān)于y軸對稱,圖象關(guān)于y軸對稱的函數(shù)一定是偶函數(shù).
(2)奇函數(shù)的圖象關(guān)于原點對稱,圖象關(guān)于原點對稱的函數(shù)一定是奇函數(shù).
1.思考辨析(正確的打“√”,錯誤的打“×”)
(1)函數(shù)f(x)=x的圖象關(guān)于(0,0)對稱. ( )
(2)偶函數(shù)的圖象一定與y軸相交. ( )
(3)若對函數(shù)f(x)有f(-1)=f(1),則f(x)為偶函數(shù). ( )
(4)奇函數(shù)的圖象一定過(0,0). ( )
[答案] (1)√ (2)× (3)× (4)×
2.若f(x)是定義在區(qū)間[a-2,5]上的奇函數(shù),則a=________.