必修1-函數(shù)的奇偶性

1、:.函函數(shù)數(shù)的的奇奇偶偶性性定定義義一一.)(),()(,),(. 1就就叫叫做做奇奇函函數(shù)數(shù)那那么么都都有有內(nèi)內(nèi)任任意意一一個(gè)個(gè)如如果果對(duì)對(duì)于于定定義義域域?qū)?duì)于于函函數(shù)數(shù)xfxfxfxIxf 函函數(shù)數(shù)的的奇奇偶偶性性.)(),()(,),(. 2就就叫叫做做偶偶函函數(shù)數(shù)那那么么都都有有內(nèi)內(nèi)任任意意一一個(gè)個(gè)如如果果對(duì)對(duì)于于定定義義域域?qū)?duì)于于函函數(shù)數(shù)xfxfxfxIxf :.價(jià)價(jià)形形式式函函數(shù)數(shù)的的奇奇偶偶性性定定義義的的等等二二1)()(0)()()()( xfxfxfxfxfxf:. 2函函數(shù)數(shù)的的奇奇偶偶性性判判斷斷方方法法:).1 利利用用定定義義;:).2看看從從左左至至右右圖圖象

2、象的的走走向向利利用用圖圖象象;,對(duì)對(duì)稱稱看看定定義義域域是是否否關(guān)關(guān)于于原原點(diǎn)點(diǎn)求求定定義義域域;)()(,的的關(guān)關(guān)系系與與則則考考察察稱稱若若定定義義域域關(guān)關(guān)于于原原點(diǎn)點(diǎn)對(duì)對(duì)xfxf :. 3 奇奇偶偶函函數(shù)數(shù)的的圖圖象象特特征征;).1圖圖象象關(guān)關(guān)于于原原點(diǎn)點(diǎn)對(duì)對(duì)稱稱奇奇函函數(shù)數(shù) ;).2軸軸對(duì)對(duì)稱稱圖圖象象關(guān)關(guān)于于偶偶函函數(shù)數(shù)yyxxOyxO2)(xxf 3)(xxf :. 4 一一些些特特殊殊函函數(shù)數(shù)的的奇奇偶偶性性0),(,)().1 mmmxaxf;)(,0是是偶偶函函數(shù)數(shù)時(shí)時(shí)當(dāng)當(dāng)xfa ;0)(,0既既是是奇奇函函數(shù)數(shù)又又是是偶偶函函數(shù)數(shù)時(shí)時(shí)當(dāng)當(dāng) xfa11).4 xxaay)

3、1lg().62 xxy)(21).2xxaay )(21).3xxaay xxya 22log).5xxy 22).7:. 5論論與與函函數(shù)數(shù)奇奇偶偶性性相相關(guān)關(guān)的的結(jié)結(jié);0)0(,)().1 fxf則則在在原原點(diǎn)點(diǎn)有有定定義義奇奇函函數(shù)數(shù);:).2偶偶偶偶偶偶偶偶偶偶偶偶偶偶奇奇奇奇奇奇奇奇奇奇在在公公共共定定義義域域內(nèi)內(nèi) ;,).3上上有有相相同同的的單單調(diào)調(diào)性性和和奇奇函函數(shù)數(shù)在在abba ;,).4上上有有相相反反的的單單調(diào)調(diào)性性和和偶偶函函數(shù)數(shù)在在abba ;0)().623 cadcxbxaxxf為為偶偶函函數(shù)數(shù)函函數(shù)數(shù);0)().723 dbdcxbxaxxf為為奇奇函函數(shù)數(shù)函

4、函數(shù)數(shù),), 0().5單單調(diào)調(diào)遞遞增增若若偶偶函函數(shù)數(shù)在在 |)()(2121xxxfxf .)(),1()(,0,)(. 1的的解解析析式式試試求求函函數(shù)數(shù)時(shí)時(shí)且且當(dāng)當(dāng)上上的的奇奇函函數(shù)數(shù)為為已已知知函函數(shù)數(shù)xfxxxfxRxf :解解, 0,0 xx時(shí)時(shí)設(shè)設(shè)),1()(xxxf ),1()(,0,)(xxxfxRxf 時(shí)時(shí)且且當(dāng)當(dāng)上上的的奇奇函函數(shù)數(shù)為為函函數(shù)數(shù)0)0(),()( fxfxf)0(),1()( xxxxf)0(),1()( xxxxf。 )0()1()0(0)0()1()(xxxxxxxxf._)3(, 8)3(, 5)()()(,)()( FFxngxmfxFRxgxf

5、則則且且若若上上的的奇奇函函數(shù)數(shù)都都是是定定義義在在與與已已知知函函數(shù)數(shù))()(),()()()(xgxgxfxfRxgxf 上上的的奇奇函函數(shù)數(shù)都都是是定定義義在在與與函函數(shù)數(shù)5)3()3()3( ngmfF5)3()3( ngmf85)3()3( ngmf3)3()3( ngmf5)3()3()3( ngmfF253 :分分析析._)3()2(, 1)2()3(,)()07.(2 ffffxfy則則若若為為奇奇函函數(shù)數(shù)已已知知函函數(shù)數(shù)遼遼寧寧._)2()1(, 3)2()1(3)1()2(,)()07.(3 ffffffxfy則則若若為為奇奇函函數(shù)數(shù)已已知知函函數(shù)數(shù)上上海海是是偶偶函函數(shù)數(shù)

6、是是偶偶函函數(shù)數(shù)是是奇奇函函數(shù)數(shù)是是奇奇函函數(shù)數(shù))()(.)()(.| )(| )(.)()(. 4xfxfDxfxfCxfxfBxfxfA bDbCbBbAafbafxxxf1.1.)()(,)(,11lg)()07.(5 則則若若已已知知函函數(shù)數(shù)遼遼寧寧32.32.32.32.)()(,23)(. 6 xyDyCxyBxyAxfyxyxfy的的表表達(dá)達(dá)式式為為則則圖圖象象關(guān)關(guān)于于原原點(diǎn)點(diǎn)對(duì)對(duì)稱稱的的的的圖圖像像與與函函數(shù)數(shù)如如果果函函數(shù)數(shù)._,121)(. 8 aaxfx則則為為奇奇函函數(shù)數(shù)已已知知函函數(shù)數(shù)._,)(1()()07.(7 aaxxxf則則為為偶偶函函數(shù)數(shù)設(shè)設(shè)函函數(shù)數(shù)寧寧夏夏

7、.)8()1)(8()(. 92的的奇奇偶偶性性判判斷斷函函數(shù)數(shù) xxxxxf._,3;1|;|; 1:.102其其中中是是偶偶函函數(shù)數(shù)的的是是已已知知下下列列函函數(shù)數(shù)xyxxyxyxy 25023|.250023|.023|.250|.)(21)(, 2)(,0,)(.11 xxxDxxxCxxBxxAxfxxfxRxfy或或或或的的解解集集是是那那么么不不等等式式時(shí)時(shí)當(dāng)當(dāng)上上的的奇奇函函數(shù)數(shù)是是定定義義在在已已知知函函數(shù)數(shù) 020002)(:xxxxxxf解解析析Oxy2 222 25023|.250023|.023|.250|.)(21)(, 2)(,0,)(.11 xxxDxxxCxxBxxAxfxxfxRxfy或或或或的的解解集集是是那那么么不不等等式式時(shí)時(shí)當(dāng)當(dāng)上上的的奇奇函函數(shù)數(shù)是是定定義義在在已已知知函函數(shù)數(shù)25023|.250023|.023|.2