第2課時(shí) 對(duì)數(shù)函數(shù)的圖象與性質(zhì)的應(yīng)用

1、1第2課時(shí)對(duì)數(shù)函數(shù)的圖象與性質(zhì)的應(yīng)用一知識(shí)導(dǎo)學(xué)一知識(shí)導(dǎo)學(xué)問(wèn)題1:對(duì)數(shù)函數(shù)y=logax(a0且a≠1)的定義域、值域和單調(diào)性(1)y=logax定義域?yàn)橹涤驗(yàn)?(2)當(dāng)01時(shí)y=logax在定義域內(nèi)是.問(wèn)題2:函數(shù)y=ax與函數(shù)y=logax(a0且a≠1)的區(qū)別與聯(lián)系(1)將函數(shù)y=ax中的字母xy對(duì)換一下就變成了函數(shù)y=logax所以稱函數(shù)y=ax與函數(shù)y=logax互為.(2)若函數(shù)y=ax圖象經(jīng)過(guò)點(diǎn)(ab)則反函數(shù)y=logax

2、圖象經(jīng)過(guò)點(diǎn)所以函數(shù)y=ax圖象與函數(shù)y=logax圖象關(guān)于直線對(duì)稱.問(wèn)題3:關(guān)于對(duì)數(shù)的不等式的解法(1)形如logaf(x)b的不等式先將其轉(zhuǎn)化為logaf(x)logaab再根據(jù)底數(shù)a的值確定函數(shù)y=logax的單調(diào)性:當(dāng)0logaab?當(dāng)a1時(shí)logaf(x)logaab?.(2)形如logaf(x)logag(x)的不等式首先要求定義域其次根據(jù)底數(shù)a的值確定函數(shù)y=logax的單調(diào)性:當(dāng)0logag(x)?當(dāng)a1時(shí)logaf(x)

3、logag(x)?.(3)形如logaf(x)clogag(x)的不等式先將其轉(zhuǎn)化為logaf(x)logag(x)c再根據(jù)(2)的解法進(jìn)行求解注意求定義域即解不等式組.問(wèn)題4:判斷復(fù)合函數(shù)y=logaf(x)的單調(diào)性.3四拓展應(yīng)用四拓展應(yīng)用1.已知a0且a≠1函數(shù)y=ax與y=loga(x)的圖象可能是下圖中的.[來(lái)源:學(xué)?？?。網(wǎng)Z。X。X。K]2.若a0且a≠1且loga(2a1)1).(1)求f(x)的定義域和值域(2)判斷并證明