新高考數(shù)學(xué)一輪復(fù)習(xí)第2章 第05講 指數(shù)與指數(shù)函數(shù) 精講+精練（學(xué)生版）

第05講指數(shù)與指數(shù)函數(shù)(精講+精練）目錄第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶第二部分：課前自我評(píng)估測(cè)試第三部分：典型例題剖析高頻考點(diǎn)一：指數(shù)與指數(shù)冪的運(yùn)算高頻考點(diǎn)二：指數(shù)函數(shù)的概念高頻考點(diǎn)三：指數(shù)函數(shù)的圖象①判斷指數(shù)型函數(shù)的圖象；②根據(jù)指數(shù)型函數(shù)圖象求參數(shù)③指數(shù)型函數(shù)圖象過(guò)定點(diǎn)問(wèn)題；④指數(shù)函數(shù)圖象應(yīng)用高頻考點(diǎn)四：指數(shù)（型）函數(shù)定義域高頻考點(diǎn)五：指數(shù)（型）函數(shù)的值域①指數(shù)函數(shù)在區(qū)間SKIPIF1<0上的值域；②指數(shù)型復(fù)合函數(shù)值域③根據(jù)指數(shù)函數(shù)值域（最值）求參數(shù)高頻考點(diǎn)六：指數(shù)函數(shù)單調(diào)性①判斷指數(shù)函數(shù)單調(diào)性；②由指數(shù)（型）函數(shù)單調(diào)性求參數(shù)③判斷指數(shù)型復(fù)合函數(shù)單調(diào)性；④比較大?、莞鶕?jù)指數(shù)函數(shù)單調(diào)性解不等式高頻考點(diǎn)七：指數(shù)函數(shù)的最值①求已知指數(shù)型函數(shù)的值域②根據(jù)指數(shù)函數(shù)最值求參數(shù)③含參指數(shù)（型）函數(shù)最值第四部分：高考真題感悟第五部分：第05講指數(shù)與指數(shù)函數(shù)（精練）第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶第一部分：知識(shí)點(diǎn)精準(zhǔn)記憶1、根式的概念及性質(zhì)（1）概念：式子SKIPIF1<0叫做根式，其中SKIPIF1<0叫做根指數(shù)，SKIPIF1<0叫做被開(kāi)方數(shù)．（2）性質(zhì)：①SKIPIF1<0(SKIPIF1<0且SKIPIF1<0)；②當(dāng)SKIPIF1<0為奇數(shù)時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0為偶數(shù)時(shí)，SKIPIF1<02、分?jǐn)?shù)指數(shù)冪①正數(shù)的正分?jǐn)?shù)指數(shù)冪的意義是SKIPIF1<0(SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0)；②正數(shù)的負(fù)分?jǐn)?shù)指數(shù)冪的意義是SKIPIF1<0(SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0)；③0的正分?jǐn)?shù)指數(shù)冪等于0；0的負(fù)分?jǐn)?shù)指數(shù)冪沒(méi)有意義．3、指數(shù)冪的運(yùn)算性質(zhì)①SKIPIF1<0；②SKIPIF1<0；③SKIPIF1<0.4、指數(shù)函數(shù)及其性質(zhì)（1）指數(shù)函數(shù)的概念函數(shù)SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)叫做指數(shù)函數(shù)，其中指數(shù)SKIPIF1<0是自變量，函數(shù)的定義域是SKIPIF1<0．（2）指數(shù)函數(shù)SKIPIF1<0的圖象和性質(zhì)底數(shù)SKIPIF1<0SKIPIF1<0圖象性質(zhì)定義域?yàn)镾KIPIF1<0，值域?yàn)镾KIPIF1<0圖象過(guò)定點(diǎn)SKIPIF1<0當(dāng)SKIPIF1<0時(shí)，恒有SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，恒有SKIPIF1<0當(dāng)SKIPIF1<0時(shí)，恒有SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，恒有SKIPIF1<0在定義域SKIPIF1<0上為增函數(shù)在定義域SKIPIF1<0上為減函數(shù)注意指數(shù)函數(shù)SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)的圖象和性質(zhì)與SKIPIF1<0的取值有關(guān)，應(yīng)分SKIPIF1<0與SKIPIF1<0來(lái)研究第二部分：課前自我評(píng)估測(cè)試第二部分：課前自我評(píng)估測(cè)試一、判斷題1．（2021·江西·貴溪市實(shí)驗(yàn)中學(xué)高二階段練習(xí)）函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖象必過(guò)定點(diǎn)SKIPIF1<0()2．（2021·江西·貴溪市實(shí)驗(yàn)中學(xué)高二階段練習(xí)）SKIPIF1<0

()二、單選題1．（2022·寧夏·銀川一中高二期末（文））函數(shù)SKIPIF1<0在SKIPIF1<0的最大值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·江蘇南通·高一期末）已知指數(shù)函數(shù)SKIPIF1<0（SKIPIF1<0，且SKIPIF1<0），且SKIPIF1<0，則SKIPIF1<0的取值范圍（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·北京·高三專題練習(xí)）若函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖像經(jīng)過(guò)定點(diǎn)P，則點(diǎn)P的坐標(biāo)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·河北廊坊·高一期末）指數(shù)函數(shù)SKIPIF1<0在R上單調(diào)遞減，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·北京·高三專題練習(xí)）若函數(shù)SKIPIF1<0是指數(shù)函數(shù)，則SKIPIF1<0等于（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0第三部分：典型例題剖析第三部分：典型例題剖析高頻考點(diǎn)一：指數(shù)與指數(shù)冪的運(yùn)算1．（2022·廣東肇慶·高一期末）設(shè)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．1 C．2 D．32．（2022·上海楊浦·高一期末）設(shè)SKIPIF1<0，下列計(jì)算中正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·廣東深圳·高一期末）下列根式與分?jǐn)?shù)指數(shù)冪的互化正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·高三專題練習(xí)）化簡(jiǎn)SKIPIF1<0的結(jié)果為（

）A．－SKIPIF1<0 B．－SKIPIF1<0C．－SKIPIF1<0 D．－6ab高頻考點(diǎn)二：指數(shù)函數(shù)的概念1．（2022·浙江·高三專題練習(xí)）函數(shù)SKIPIF1<0，且a≠1)的圖象經(jīng)過(guò)點(diǎn)SKIPIF1<0，則f(-2)=（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．92．（2022·黑龍江·嫩江市第一中學(xué)校高一期末）已知指數(shù)函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則SKIPIF1<0的值為（

）A．3 B．2 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·高一課時(shí)練習(xí)）函數(shù)SKIPIF1<0是指數(shù)函數(shù)，則（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0且SKIPIF1<04．（2022·浙江·高三專題練習(xí)）若指數(shù)函數(shù)SKIPIF1<0在[－1,1]上的最大值與最小值的差是1，則底數(shù)a等于A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0高頻考點(diǎn)三：指數(shù)函數(shù)的圖象①判斷指數(shù)型函數(shù)的圖象1．（2022·上海市復(fù)興高級(jí)中學(xué)高一階段練習(xí)）函數(shù)SKIPIF1<0的大致圖像是（

）A．B．C．D．2．（2022·上海市進(jìn)才中學(xué)高二階段練習(xí)）函數(shù)SKIPIF1<0的圖像的大致形狀是（

）A． B．C．D．3．（2022·全國(guó)·高三專題練習(xí)）已知0＜m＜n＜1，則指數(shù)函數(shù)①y＝mx，②y＝nx的圖象為（）．A． B．C．D．4．（2022·全國(guó)·高三專題練習(xí)（文））函數(shù)SKIPIF1<0的圖象可能是

()A． B．C． D．②根據(jù)指數(shù)型函數(shù)圖象求參數(shù)1．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的圖象如圖所示，其中SKIPIF1<0，SKIPIF1<0為常數(shù)，則下列結(jié)論正確的是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<02．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0與SKIPIF1<0的圖象如圖，則下列不等式一定成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·全國(guó)·高一專題練習(xí)）函數(shù)SKIPIF1<0的圖像如圖所示，其中SKIPIF1<0SKIPIF1<0為常數(shù)，則下列結(jié)論正確的是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<04．（2021·全國(guó)·高一專題練習(xí)）若函數(shù)SKIPIF1<0的圖象如圖所示，則（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0③指數(shù)型函數(shù)圖象過(guò)定點(diǎn)問(wèn)題1．（2022·吉林·長(zhǎng)春市第二中學(xué)高一期末）函數(shù)SKIPIF1<0且SKIPIF1<0的圖象恒過(guò)定點(diǎn)（

）A．(－2，0) B．(－1，0)C．(0，－1) D．(－1，－2)2．（2022·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0過(guò)定點(diǎn)SKIPIF1<0，以SKIPIF1<0為頂點(diǎn)且過(guò)原點(diǎn)的二次函數(shù)SKIPIF1<0的解析式為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·河南焦作·高一期末）已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖象過(guò)定點(diǎn)SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0(SKIPIF1<0，SKIPIF1<0)恒過(guò)定點(diǎn)SKIPIF1<0，則函數(shù)SKIPIF1<0的圖像不經(jīng)過(guò)（

）A．第一象限 B．第二象限C．第三象限 D．第四象限④指數(shù)函數(shù)圖象應(yīng)用1．（2021·重慶市涪陵第二中學(xué)校高一階段練習(xí)）函數(shù)SKIPIF1<0的圖象可能是（

）A． B．C． D．2．（2021·全國(guó)·高一課時(shí)練習(xí)）函數(shù)SKIPIF1<0，且SKIPIF1<0）與SKIPIF1<0的圖像大致是A． B． C． D．3．（2021·全國(guó)·高一課時(shí)練習(xí)）若SKIPIF1<0，SKIPIF1<0，則函數(shù)SKIPIF1<0的圖像一定經(jīng)過(guò)（

）A．第一、二、三象限 B．第一、三、四象限C．第二、三、四象限 D．第一、二、四象限高頻考點(diǎn)四：指數(shù)（型）函數(shù)定義域1．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的定義域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的定義域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2021·江蘇·高一專題練習(xí)）函數(shù)y＝SKIPIF1<0的定義域是(－∞，0]，則a的取值范圍為()A．a(chǎn)＞0 B．a(chǎn)＜1C．0＜a＜1 D．a(chǎn)≠14．（2021·廣西河池·高一階段練習(xí)）設(shè)函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的定義域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0高頻考點(diǎn)五：指數(shù)（型）函數(shù)的值域①指數(shù)函數(shù)在區(qū)間SKIPIF1<0上的值域1．（2022·全國(guó)·高一）當(dāng)xSKIPIF1<0[-1，1]時(shí)，函數(shù)f(x)=3x-2的值域?yàn)開(kāi)_______2．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)f（x）=9x﹣aSKIPIF1<03x+1+a2（x∈[0，1]，a∈R），記f（x）的最大值為g（a）．（Ⅰ）求g（a）解析式；（Ⅱ）若對(duì)于任意t∈[﹣2，2]，任意a∈R，不等式g（a）≥﹣m2+tm恒成立，求實(shí)數(shù)m的范圍．3．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0.當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0在SKIPIF1<0的值域；4．（2022·江西省豐城中學(xué)高一開(kāi)學(xué)考試）函數(shù)SKIPIF1<0且SKIPIF1<0，函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的解析式；(2)若關(guān)于SKIPIF1<0的方程SKIPIF1<0在區(qū)間SKIPIF1<0上有實(shí)數(shù)根，求實(shí)數(shù)SKIPIF1<0的取值范圍.②指數(shù)型復(fù)合函數(shù)值域1．（2022·山西·臨汾第一中學(xué)校高一期末）函數(shù)SKIPIF1<0的值域?yàn)椋?/p>

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·湖南邵陽(yáng)·高一期末）函數(shù)SKIPIF1<0的值域?yàn)開(kāi)_____．3．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的值域是___________.4．（2022·河南·洛寧縣第一高級(jí)中學(xué)高一階段練習(xí)）已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的值域；(2)若SKIPIF1<0有最大值16，求SKIPIF1<0的值.5．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0.（1）求SKIPIF1<0在SKIPIF1<0上的值域；③根據(jù)指數(shù)函數(shù)值域（最值）求參數(shù)1．（2022·廣東湛江·高一期末）已知函數(shù)SKIPIF1<0的定義域和值域都是SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．SKIPIF1<02．（2022·遼寧鞍山·高一期末）若函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國(guó)·高一）已知函數(shù)SKIPIF1<0且SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值比最小值大SKIPIF1<0,求SKIPIF1<0的值.4．（2022·湖南·高一期末）已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的值域；(2)當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值為7，求SKIPIF1<0的值.5．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)，SKIPIF1<0）是SKIPIF1<0上的奇函數(shù)．(1)求實(shí)數(shù)SKIPIF1<0的值；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的值域?yàn)镾KIPIF1<0，求SKIPIF1<0的值．高頻考點(diǎn)六：指數(shù)函數(shù)單調(diào)性①判斷指數(shù)函數(shù)單調(diào)性1．（2022·廣西南寧·高一期末）設(shè)函數(shù)SKIPIF1<0，則SKIPIF1<0（

）A．是偶函數(shù)，且在SKIPIF1<0單調(diào)遞增 B．是偶函數(shù)，且在SKIPIF1<0單調(diào)遞減C．是奇函數(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2．（2022·福建寧德·高一期末）已知SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0．(1)求SKIPIF1<0的解析式；(2)判斷SKIPIF1<0的單調(diào)性，并根據(jù)定義證明．3．（2021·貴州·六盤(pán)水紅橋?qū)W校高一階段練習(xí)）若函數(shù)SKIPIF1<0是指數(shù)函數(shù)(1)求SKIPIF1<0，SKIPIF1<0的值；(2)求解不等式SKIPIF1<04．（2021·全國(guó)·高一期末）設(shè)函數(shù)SKIPIF1<0，(1)判斷SKIPIF1<0的單調(diào)性，并證明你的結(jié)論；②由指數(shù)（型）函數(shù)單調(diào)性求參數(shù)1．（2022·遼寧朝陽(yáng)·高一開(kāi)學(xué)考試）若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·內(nèi)蒙古·赤峰二中高一期末（文））若函數(shù)SKIPIF1<0是R上的減函數(shù)，則實(shí)數(shù)a的取值范圍是___．3．（2022·河北張家口·高一期末）已知函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是______.4．（2022·湖南·高一課時(shí)練習(xí)）若函數(shù)SKIPIF1<0是指數(shù)函數(shù)，且為指數(shù)增長(zhǎng)型函數(shù)模型，則實(shí)數(shù)SKIPIF1<0________.5．（2022·安徽·歙縣教研室高一期末）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上為增函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍為_(kāi)_____.6．（2022·湖南·高一課時(shí)練習(xí)）若函數(shù)SKIPIF1<0是區(qū)間SKIPIF1<0上的減函數(shù)，求實(shí)數(shù)SKIPIF1<0的取值范圍．③判斷指數(shù)型復(fù)合函數(shù)單調(diào)性1．（2022·安徽省蚌埠第三中學(xué)高一開(kāi)學(xué)考試）函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南·商丘市第一高級(jí)中學(xué)高一開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0，且對(duì)于任意的SKIPIF1<0，都有SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·寧夏·吳忠中學(xué)高一期末）已知函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是______．4．（2022·河南·林州一中高一開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0是奇函數(shù).(1)求SKIPIF1<0的值；(2)判斷并證明函數(shù)SKIPIF1<0的單調(diào)性.④比較大小1．（2022·廣東汕尾·高一期末）若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·陜西·略陽(yáng)縣天津高級(jí)中學(xué)高三階段練習(xí)（文））設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·福建三明·高一期末）已知SKIPIF1<0，則它們的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·海南·模擬預(yù)測(cè)）設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0⑤根據(jù)指數(shù)函數(shù)單調(diào)性解不等式1．（2022·全國(guó)·高一）若SKIPIF1<0，則x的取值范圍是______．2．（2022·海南鑫源高級(jí)中學(xué)高一期末）已知不等式SKIPIF1<0的解集是__________.3．（2022·福建·莆田一中高一開(kāi)學(xué)考試）已知SKIPIF1<0是定義在R上的偶函數(shù)，且在區(qū)間SKIPIF1<0上單調(diào)遞增，若實(shí)數(shù)SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是______．4．（2022·福建福州·高一期末）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．(1)求SKIPIF1<0的解析式；(2)解不等式SKIPIF1<0．高頻考點(diǎn)七：指數(shù)函數(shù)的最值①求已知指數(shù)型函數(shù)的值域1．（2022·新疆·石河子第二中學(xué)高二階段練習(xí)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·北京·高三學(xué)業(yè)考試）已知函數(shù)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．有最大值，有最小值 B．有最大值，無(wú)最小值C．無(wú)最大值，有最小值 D．無(wú)最大值，無(wú)最小值3．（2022·全國(guó)·高三專題練習(xí)（文））設(shè)函數(shù)SKIPIF1<0，則SKIPIF1<0________；函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0的最大值為_(kāi)________．4．（2022·貴州貴陽(yáng)·高一期末）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)a的取值范圍是___________.5．（2022·甘肅·蘭州一中高一期末）已知SKIPIF1<0，則函數(shù)SKIPIF1<0的最大值為_(kāi)_________.②根據(jù)指數(shù)函數(shù)最值求參數(shù)1．（2022·遼寧·渤海大學(xué)附屬高級(jí)中學(xué)高一期末）若函數(shù)SKIPIF1<0在SKIPIF1<0上有最大值SKIPIF1<0，則實(shí)數(shù)a的值為（

）A．1 B．SKIPIF1<0 C．1或SKIPIF1<0 D．1或SKIPIF1<02．(多選）（2022·江蘇常州·高一期末）若函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在區(qū)間SKIPIF1<0上的最大值和最小值的和為SKIPIF1<0，則SKIPIF1<0的值可能是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·上海虹口·高一期末）已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在SKIPIF1<0的最大值與最小值之差等于SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的值為_(kāi)_____．4．（2022·青?！ずＤ喜刈遄灾沃莞呒?jí)中學(xué)高一期末）已知指數(shù)函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在區(qū)間SKIPIF1<0上的最大值是最小值的2倍，則SKIPIF1<0______．5．（2022·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值之和為6，則實(shí)數(shù)SKIPIF1<0______.6．（2022·湖南·高一課時(shí)練習(xí)）若函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在區(qū)間SKIPIF1<0上的最小值為SKIPIF1<0，求SKIPIF1<0的值．③含參指數(shù)（型）函數(shù)最值1．（2022·全國(guó)·高三專題練習(xí)）如果函數(shù)y=a2x+2ax-1(a>0，且a≠1)在區(qū)間[-1，1]上的最大值是14，則a的值為_(kāi)_______.2．（2022·寧夏吳忠區(qū)青銅峽市教育局高一開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0．（1）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的零點(diǎn)；（2）若SKIPIF1<0，求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值SKIPIF1<0．3．（2022·全國(guó)·高三專題練習(xí)（文））已知函數(shù)SKIPIF1<0．（1）若函數(shù)SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上有最大值SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的值；（2）若方程SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上有解，求實(shí)數(shù)SKIPIF1<0的取值范圍．4．（2022·全國(guó)·高一課時(shí)練習(xí)）求函數(shù)SKIPIF1<0的最值.第四部分：高考真題感悟第四部分：高考真題感悟1．（2020·山東·高考真題）已知函數(shù)SKIPIF1<0是偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則該函數(shù)在SKIPIF1<0上的圖像大致是（

）A． B．C． D．2．（2021·湖南·高考真題）已知函數(shù)SKIPIF1<0（1）畫(huà)出函數(shù)SKIPIF1<0的圖象；（2）若SKIPIF1<0，求SKIPIF1<0的取值范圍.第五部分：第05講指數(shù)與指數(shù)函數(shù)（精練）第五部分：第05講指數(shù)與指數(shù)函數(shù)（精練）一、單選題1．（2022·江蘇江蘇·一模）設(shè)全集SKIPIF1<0，集合SKIPIF1<0，SKIPIF1<0，則集合SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南·模擬預(yù)測(cè)（文））已知SKIPIF1<0，SKIPIF1<0，則ab=（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0 D．13．（2022·遼寧朝陽(yáng)·高二開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則a，b，c的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·四川宜賓·二模（文））物理學(xué)家和數(shù)學(xué)家牛頓（IssacNewton）提出了物體在常溫下溫度變化的冷卻模型：設(shè)物體的初始溫度是SKIPIF1<0（單位：SKIPIF1<0），環(huán)境溫度是SKIPIF1<0（單位：SKIPIF1<0），且經(jīng)過(guò)一定時(shí)間SKIPIF1<0（單位：SKIPIF1<0）后物體的溫度SKIPIF1<0（單位：SKIPIF1<0）滿足SKIPIF1<0（SKIPIF1<0為正常數(shù)）.現(xiàn)有一杯100SKIPIF1<0熱水，環(huán)境溫度SKIPIF1<0℃，冷卻到40℃需要SKIPIF1<0，那么這杯熱水要從SKIPIF1<0SKIPIF1<0繼續(xù)冷卻到SKIPIF1<0SKIPIF1<0，還需要的時(shí)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·湖北·石首市第一中學(xué)高一階段練習(xí)）已知函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·河南·模擬預(yù)測(cè)（文