高中數(shù)學(xué)必修基本初等函數(shù)?？碱}型對(duì)數(shù)函數(shù)的圖象及性質(zhì)

1、對(duì)數(shù)函數(shù)的圖象及性質(zhì)對(duì)數(shù)函數(shù)的圖象及性質(zhì)【知識(shí)梳理】1對(duì)數(shù)函數(shù)的定義函數(shù)(，且)叫做對(duì)數(shù)函數(shù)，其中是自變量，函數(shù)的定義域是logayx?0a?1a?x??0??2對(duì)數(shù)函數(shù)的圖象與性質(zhì)1a?01a??圖象定義域：??0??值域：R過(guò)點(diǎn)，即當(dāng)時(shí)，??101x?0y?性質(zhì)在上是增函數(shù)??0??在上是減函數(shù)??0??3對(duì)數(shù)函數(shù)與指數(shù)函數(shù)的關(guān)系指數(shù)函數(shù)和對(duì)數(shù)函數(shù)(，且)互為反函數(shù)xya?logayx?0a?1a?【?？碱}型】題型一、對(duì)數(shù)函數(shù)的概念

2、【例1】判斷下列函數(shù)是否是對(duì)數(shù)函數(shù)？并說(shuō)明理由①(，且)；2logayx?0a?1a?②；2log1yx??③；82logyx?④(，且)；logxya?0x?1x?⑤.5logyx?[解]∵①中真數(shù)不是自變量，x∴不是對(duì)數(shù)函數(shù)；∵②中對(duì)數(shù)式后減，∴不是對(duì)數(shù)函數(shù)；1的底數(shù).logdyx?01c??01d??過(guò)點(diǎn)作平行于軸的直線，則直線與四條曲線交點(diǎn)的橫坐標(biāo)從左向右依次為，??01xc，，，顯然.dab1badc????[答案](1)(2

3、)??02?1badc????【類題通法】1對(duì)數(shù)函數(shù)圖象過(guò)定點(diǎn)問(wèn)題求函數(shù)(，且)的圖象過(guò)的定點(diǎn)時(shí)，只需令求出，??logaymfx??0a?1a???1fx?x即得定點(diǎn)為??xm2對(duì)數(shù)函數(shù)圖象的判斷根據(jù)對(duì)數(shù)函數(shù)圖象判斷底數(shù)大小的方法：作直線與所給圖象相交，交點(diǎn)的橫坐標(biāo)即為各個(gè)底數(shù)，依據(jù)在第一象限內(nèi)，自左向1y?右，圖象對(duì)應(yīng)的對(duì)數(shù)函數(shù)的底數(shù)逐漸變大，可比較底數(shù)的大小【對(duì)點(diǎn)訓(xùn)練】已知，且，則函數(shù)與的圖象只能是()0a?1a?xya???lo

4、gayx??解析：選B法一：若，則函數(shù)的圖象下降且過(guò)點(diǎn)，而函數(shù)01a??xya???01的圖象上升且過(guò)點(diǎn)，以上圖象均不符合??logayx????10?若，則函數(shù)的圖象上升且過(guò)點(diǎn)，而函數(shù)的圖象下降且過(guò)1a?xya???01??logayx??點(diǎn)，只有B中圖象符合??10?法二：首先指數(shù)函數(shù)的圖象只可能在上半平面，函數(shù)的圖象只可能xya???logayx??在左半平面，從而排除A，C；再看單調(diào)性，與的單調(diào)性正好相反，排除xya???log