新高考數(shù)學(xué)一輪復(fù)習(xí)考點(diǎn)精講練+易錯(cuò)題型第13講 對(duì)數(shù)函數(shù)（原卷版）

對(duì)數(shù)函數(shù)【基礎(chǔ)知識(shí)網(wǎng)絡(luò)圖】對(duì)數(shù)與對(duì)數(shù)函數(shù)對(duì)數(shù)與對(duì)數(shù)函數(shù)圖象與性質(zhì)對(duì)數(shù)運(yùn)算性質(zhì)對(duì)數(shù)函數(shù)的圖像與性質(zhì)對(duì)數(shù)的概念指對(duì)互化運(yùn)算【基礎(chǔ)知識(shí)全通關(guān)】知識(shí)點(diǎn)01對(duì)數(shù)函數(shù)及其性質(zhì)(1)概念：函數(shù)y＝logax(a>0，且a≠1)叫做對(duì)數(shù)函數(shù)，其中x是自變量，函數(shù)的定義域是(0，＋∞).(2)對(duì)數(shù)函數(shù)的圖象與性質(zhì)a>10<a<1圖象性質(zhì)定義域：(0，＋∞)值域：R當(dāng)x＝1時(shí)，y＝0，即過(guò)定點(diǎn)(1，0)當(dāng)x>1時(shí)，y>0；當(dāng)0<x<1時(shí)，y<0當(dāng)x>1時(shí)，y<0；當(dāng)0<x<1時(shí)，y>0在(0，＋∞)上是增函數(shù)在(0，＋∞)上是減函數(shù)知識(shí)點(diǎn)02反函數(shù)對(duì)數(shù)函數(shù)y＝logax(a＞0，且a≠1)和指數(shù)函數(shù)y＝ax(a＞0，且a≠1)互為反函數(shù)，它們的圖象關(guān)于直線y＝x對(duì)稱．【知識(shí)拓展】1.換底公式的兩個(gè)重要結(jié)論(1)logab＝eq\f(1,logba)；(2)logambn＝eq\f(n,m)logab.其中a>0，且a≠1，b>0，且b≠1，m，n∈R.2.在第一象限內(nèi)，不同底的對(duì)數(shù)函數(shù)的圖象從左到右底數(shù)逐漸增大.3.對(duì)數(shù)函數(shù)y＝logax(a>0，且a≠1)的圖象過(guò)定點(diǎn)(1，0)，且過(guò)點(diǎn)(a，1)，eq\b\lc\(\rc\)(\a\vs4\al\co1(\f(1,a)，－1))，函數(shù)圖象只在第一、四象限.【考點(diǎn)研習(xí)一點(diǎn)通】考點(diǎn)01：對(duì)數(shù)函數(shù)的概念與圖象【典例1】函數(shù)與函數(shù)在同一坐標(biāo)系的圖像只可能是（）A．B．C．D．【典例2】在同一直角坐標(biāo)系中，函數(shù)且的圖象可能是（）A．B．C．D．【典例3】在同直角坐標(biāo)系中，SKIPIF1<0與SKIPIF1<0的圖象可能是（）A． B．C． D．考點(diǎn)02：對(duì)數(shù)函數(shù)的性質(zhì)及應(yīng)用【典例4】設(shè)SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【典例5】若，則（）A． B． C． D．考點(diǎn)03：對(duì)數(shù)函數(shù)的性質(zhì)及應(yīng)用【典例6】若函數(shù)則函數(shù)的值域是（）A． B． C． D．【典例7】滿足，且在單調(diào)遞減，若，，，則，，的大小關(guān)系為（）A． B．C． D．【典例8】【多選題】若實(shí)數(shù)SKIPIF1<0，則下列不等式中一定成立的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【典例9】函數(shù)的定義域?yàn)椋镜淅?0】已知函數(shù)SKIPIF1<0，則SKIPIF1<0單調(diào)遞增區(qū)間為_(kāi)_________；若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)，則a的取值范圍為_(kāi)_________．【考點(diǎn)易錯(cuò)】1.已知，若正實(shí)數(shù)滿足，則的取值范圍為（）A． B．或C．或 D．2．已知函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03.已知定義在R上的函數(shù)在區(qū)間上單調(diào)遞增，且的圖象關(guān)于對(duì)稱，若實(shí)數(shù)a滿足，則a的取值范圍是（）A． B． C． D．4.如圖為函數(shù)SKIPIF1<0）的部分圖象，已知SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的取值范圍為_(kāi)_____．【鞏固提升】1．函數(shù)SKIPIF1<0的圖象大致是（）A．B．C．D．2．已知函數(shù)f(x)＝SKIPIF1<0則函數(shù)y＝f(1－x)的大致圖象是（）A． B．C． D．3．如圖，直線SKIPIF1<0與函數(shù)SKIPIF1<0和SKIPIF1<0的圖象分別交于點(diǎn)SKIPIF1<0，SKIPIF1<0，若函數(shù)SKIPIF1<0的圖象上存在一點(diǎn)SKIPIF1<0，使得SKIPIF1<0為等邊三角形，則SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04.設(shè)函數(shù)SKIPIF1<0，則f(x)（）A．是偶函數(shù)，且在SKIPIF1<0單調(diào)遞增 B．是奇函數(shù)，且在SKIPIF1<0單調(diào)遞減C．是偶函數(shù)，且在SKIPIF1<0單調(diào)遞增 D．是奇函數(shù)，且在SKIPIF1<0單調(diào)遞減5.設(shè)是定義域?yàn)镽的偶函數(shù)，且在單調(diào)遞減，則A．（log3）＞（）＞（）B．（log3）＞（）＞（）C．（）＞（）＞（log3）D．（）＞（）＞（log3）6．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的大小關(guān)系正確的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．【多選題】若正實(shí)數(shù)a，b滿足SKIPIF1<0且SKIPIF1<0，下列不等式恒成立的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，函數(shù)SKIPIF1<0，則SKIPIF1<0__________．9．已知函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為_(kāi)__________.10．求函數(shù)y=SKIPIF1<0(-x2+2x+3)的值域和單調(diào)區(qū)間.11.判斷下列函數(shù)的奇偶性.(1)SKIPIF1<0(2)SKIPIF1<0.12．已知函數(shù)SKIPIF1<0為奇函