奇偶性中職數(shù)學(xué)

1、1)x(fy xy-5 -4 -3 -2.5 -1 1 2 3 4 5O321-1-2增區(qū)間增區(qū)間減區(qū)間減區(qū)間-4-4，-3-3 -2.5-2.5，2244，55-5-5，-4-4 -3-3，-2.5-2.5 22，4423Xy.112131212313121231()fxxyxO 1-11-1( 3)f (3)f1313( 2)f ( 1)f ()fx( )f x(1)f(2)f 一般地一般地,如果對(duì)于函數(shù)如果對(duì)于函數(shù)f(x)的定義域內(nèi)任意一個(gè)的定義域內(nèi)任意一個(gè)x,都有都有:稱稱f(x)為為奇函數(shù)奇函數(shù)4()fx( )f x-x0yxOx0圖象是以坐標(biāo)原點(diǎn)為對(duì)稱中心

2、的中心對(duì)稱圖形坐標(biāo)原點(diǎn)對(duì)稱中心圖象關(guān)于原點(diǎn)對(duì)稱y0-y0(x0,y0)(-x0,-y0)5( 2)f (2)f2()fxx( 3)f (3)f99( 1)f ()fx( )f x(1)f 一般地一般地,如果對(duì)于函數(shù)如果對(duì)于函數(shù)f(x)的定義域內(nèi)任意一個(gè)的定義域內(nèi)任意一個(gè)x,都有都有:稱稱f(x)為為偶函數(shù)偶函數(shù)xy0123-1-2-3123456789Xy.321012394101496xy0123-1-2-3123456789()fx( )f x圖象是以主y軸為對(duì)稱軸的軸對(duì)稱圖形y軸對(duì)稱軸圖象關(guān)于y軸對(duì)稱7性質(zhì)性質(zhì)奇函數(shù)奇函數(shù)偶函數(shù)偶函數(shù)定義圖象()fx( )f x關(guān)于y軸對(duì)稱()fx( )

3、f x關(guān)于原點(diǎn)對(duì)稱8判斷下列函數(shù)的奇偶性351. ( )f xx xx ,xR 對(duì)于任意都有()fx35() ()()xxx 35x xx 35()x xx( )f x()fx( )f x35( )f xxxx 是奇函數(shù)1奇函數(shù)每一項(xiàng)的指數(shù)都是奇數(shù)9判斷下列函數(shù)的奇偶性422.( )1f xxx,xR 對(duì)于任意都有()fx42()()1xx 421xx( )f x()fx( )f x42( )f xxx+1是偶函數(shù)0 x偶函數(shù)每一項(xiàng)的指數(shù)都是偶數(shù)10判斷下列函數(shù)的奇偶性3.( )1f xx ,xR 對(duì)于任意都有()fx1x ()( )fxf x()( )fxf x( )f xx+1既不是奇函數(shù)

4、也不是偶函數(shù)10 xx11判斷下列函數(shù)的奇偶性24.( ), 1,2f xx x 1,2x ( )f xx+1既不是奇函數(shù)也不是偶函數(shù) 1,2關(guān)于原點(diǎn)不對(duì)稱12判斷下列函數(shù)的奇偶性241.( )23f xxx22.( ) 1 32f xxx 33.( )3f xx x244.( ),( 3,3f xxx x 作業(yè)作業(yè): : P P5858 2 213用用 填空填空 2 2 已知函數(shù)已知函數(shù)f(x)f(x)在區(qū)間在區(qū)間-10-10，1010上是上是増増函函數(shù)數(shù)1 1 已知函數(shù)已知函數(shù)f(x)f(x)在區(qū)間（在區(qū)間（-20,20-20,20）上是減函數(shù)）上是減函數(shù)(1) f(-2)_f(-3)(1) f(-2)_f(-3)(2) f(5.1)_f(5.01)(2) f(5.1)_f(5.01)(3) f(6)_f(-1)(3) f(6)_f(-1)(4) f(-1)_f(2)(4) f(-1)_f(2) (1) f(5)_f(-5)(1) f(5)_f(-5)(2) f(-1)_f(-1.2)(2) f(