答案第=page11頁(yè)，共=sectionpages22頁(yè)專題06函數(shù)的圖像、方程與零點(diǎn)【練基礎(chǔ)】一、單選題1．（2022·安徽·六安市裕安區(qū)新安中學(xué)高三階段練習(xí)）函數(shù)SKIPIF1<0的圖象大致為（

）A． B．C． D．2．（2022·安徽·安慶一中高三階段練習(xí)（文））已知函數(shù)SKIPIF1<0則方程SKIPIF1<0的解的個(gè)數(shù)是（

）A．0 B．1 C．2 D．33．（2022·甘肅·高臺(tái)縣第一中學(xué)高三階段練習(xí)（文））如圖，SKIPIF1<0是邊長(zhǎng)為2的正三角形，記SKIPIF1<0位于直線SKIPIF1<0左側(cè)的圖形的面積為SKIPIF1<0，則SKIPIF1<0的函數(shù)圖象是（

）.A．B．C． D．4．（2023·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的圖像與函數(shù)SKIPIF1<0的圖像的交點(diǎn)個(gè)數(shù)為（

）A．2 B．3 C．4 D．05．（2021·云南省楚雄天人中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，在區(qū)間SKIPIF1<0上單調(diào)遞減，且SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<06．（2021·甘肅省民樂(lè)縣第一中學(xué)高三階段練習(xí)（理））函數(shù)SKIPIF1<0在SKIPIF1<0的零點(diǎn)個(gè)數(shù)為（）A．2 B．3 C．4 D．57．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的所有零點(diǎn)之和為（

）A．0 B．2 C．4 D．68．（2022·河南·高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0有4個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2021·重慶市第十一中學(xué)校高三階段練習(xí)）關(guān)于函數(shù)SKIPIF1<0，正確的說(shuō)法是（

）A．SKIPIF1<0有且僅有一個(gè)零點(diǎn)B．SKIPIF1<0在定義域內(nèi)單調(diào)遞減C．SKIPIF1<0的定義域?yàn)镾KIPIF1<0D．SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對(duì)稱10．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKIPIF1<0為奇函數(shù) B．SKIPIF1<0為減函數(shù)C．SKIPIF1<0有且只有一個(gè)零點(diǎn) D．SKIPIF1<0的值域?yàn)镾KIPIF1<011．（2022·湖南省祁東縣育賢中學(xué)高三階段練習(xí)）如圖是函數(shù)SKIPIF1<0的部分圖像，則（

）A．SKIPIF1<0的最小正周期為SKIPIF1<0B．將函數(shù)SKIPIF1<0的圖像向右平移SKIPIF1<0個(gè)單位后，得到的函數(shù)為奇函數(shù)C．SKIPIF1<0是函數(shù)SKIPIF1<0的一條對(duì)稱軸D．若函數(shù)SKIPIF1<0在SKIPIF1<0上有且僅有兩個(gè)零點(diǎn)，則SKIPIF1<012．（2021·福建·福清西山學(xué)校高三階段練習(xí)）已知函數(shù)SKIPIF1<0若函數(shù)SKIPIF1<0恰有2個(gè)零點(diǎn)，則實(shí)數(shù)m可以是（

）A．SKIPIF1<0 B．0 C．1 D．2三、填空題13．（2020·廣東·北京師范大學(xué)珠海分校附屬外國(guó)語(yǔ)學(xué)校高三階段練習(xí)）若函數(shù)f(x)＝x2-ax-b的兩個(gè)零點(diǎn)分別是是2和3，則函數(shù)g(x)＝bx2-ax-1的零點(diǎn)為_(kāi)___________.14．（2022·全國(guó)·高三專題練習(xí)（理））若函數(shù)SKIPIF1<0的一個(gè)零點(diǎn)為SKIPIF1<0，則常數(shù)SKIPIF1<0的一個(gè)取值為_(kāi)__________.15．（2021·福建省南平市高級(jí)中學(xué)高三階段練習(xí)）若方程SKIPIF1<0的實(shí)根在區(qū)間SKIPIF1<0上，則SKIPIF1<0_______.16．（2022·北京·北師大實(shí)驗(yàn)中學(xué)高三階段練習(xí)）若函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍是_____.四、解答題17．（2021·寧夏·青銅峽市寧朔中學(xué)高三階段練習(xí)（文））若函數(shù)SKIPIF1<0．（1）在所給的坐標(biāo)系內(nèi)畫(huà)出函數(shù)SKIPIF1<0圖像；（2）求方程SKIPIF1<0恰有三個(gè)不同實(shí)根時(shí)的實(shí)數(shù)SKIPIF1<0的取值范圍．18．（2022·河南·模擬預(yù)測(cè)（文））已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)在給出的平面直角坐標(biāo)系中畫(huà)出SKIPIF1<0和SKIPIF1<0的圖象；(2)若關(guān)于x的不等式SKIPIF1<0恒成立，求實(shí)數(shù)a的取值范圍．19．（2020·內(nèi)蒙古·巴彥淖爾市臨河區(qū)第三中學(xué)高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0，SKIPIF1<0.（1）求SKIPIF1<0的解析式.（2）若方程SKIPIF1<0有實(shí)數(shù)根，求實(shí)數(shù)a的取值范圍.20．（2022·山東省青島第九中學(xué)高三階段練習(xí)）已知函數(shù)SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程為SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間，(2)若函數(shù)SKIPIF1<0有三個(gè)零點(diǎn)，求實(shí)數(shù)m的取值范圍．21．（2021·貴州·遵義一中高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0．（1）若函數(shù)SKIPIF1<0在范圍SKIPIF1<0上存在零點(diǎn)，求SKIPIF1<0的取值范圍；（2）當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0的最小值SKIPIF1<0．22．（2020·江蘇省盱眙中學(xué)高三階段練習(xí)）已知SKIPIF1<0是偶函數(shù)．（1）求SKIPIF1<0的值；（2）若函數(shù)SKIPIF1<0的圖象與直線SKIPIF1<0有公共點(diǎn)，求a的取值范圍．【提能力】一、單選題1．（2020·全國(guó)·高三專題練習(xí)（文））函數(shù)SKIPIF1<0的圖像大致為()A． B．C． D．2．（2019·全國(guó)·高三專題練習(xí)）如圖所示，設(shè)點(diǎn)SKIPIF1<0是單位圓上的一定點(diǎn)，動(dòng)點(diǎn)SKIPIF1<0從點(diǎn)SKIPIF1<0出發(fā)在圓上按逆時(shí)針?lè)较蛐D(zhuǎn)一周，點(diǎn)SKIPIF1<0所旋轉(zhuǎn)過(guò)的SKIPIF1<0的長(zhǎng)為SKIPIF1<0，弦SKIPIF1<0的長(zhǎng)為SKIPIF1<0，則函數(shù)SKIPIF1<0的圖象大致是（

）A． B．C． D．3．（2008·四川·高考真題（理））直線SKIPIF1<0繞原點(diǎn)逆時(shí)針旋轉(zhuǎn)SKIPIF1<0，再向右平移１個(gè)單位，所得到的直線為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·高三專題練習(xí)）定義在R上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若關(guān)于x的方程SKIPIF1<0至少有8個(gè)實(shí)數(shù)解，則實(shí)數(shù)m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2021·全國(guó)·高三專題練習(xí)）如圖，函數(shù)SKIPIF1<0的圖象由一條射線和拋物線的一部分構(gòu)成，SKIPIF1<0的零點(diǎn)為SKIPIF1<0，若不等式SKIPIF1<0對(duì)SKIPIF1<0恒成立，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023·全國(guó)·高三專題練習(xí)）正實(shí)數(shù)SKIPIF1<0滿足SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0之間的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·全國(guó)·高三專題練習(xí)）設(shè)函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)個(gè)數(shù)為（

）A．1個(gè) B．2個(gè) C．3個(gè) D．4個(gè)8．（2020·全國(guó)·高三專題練習(xí)（理））已知定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0時(shí)，SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上的所有零點(diǎn)之和為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題9．（2023·全國(guó)·高三專題練習(xí)）對(duì)任意兩個(gè)實(shí)數(shù)SKIPIF1<0，定義SKIPIF1<0若SKIPIF1<0，SKIPIF1<0，下列關(guān)于函數(shù)SKIPIF1<0的說(shuō)法正確的是（

）A．函數(shù)SKIPIF1<0是偶函數(shù)B．方程SKIPIF1<0有三個(gè)解C．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增D．函數(shù)SKIPIF1<0有4個(gè)單調(diào)區(qū)間10．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有四個(gè)不同的實(shí)根SKIPIF1<0，滿足SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．函數(shù)SKIPIF1<0的零點(diǎn)為SKIPIF1<011．（2022·山東·日照國(guó)開(kāi)中學(xué)高三階段練習(xí)）已知SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則下列說(shuō)法正確的是（

）A．SKIPIF1<0是以SKIPIF1<0為周期的周期函數(shù)B．SKIPIF1<0C．函數(shù)SKIPIF1<0的圖象與函數(shù)SKIPIF1<0的圖象有且僅有SKIPIF1<0個(gè)交點(diǎn)D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<012．（2020·全國(guó)·高三專題練習(xí)）已知函數(shù)f（x）＝x，g（x）＝x－4，則下列結(jié)論正確的是（

）A．若h（x）＝f（x）g（x），則函數(shù)h（x）的最小值為4B．若h（x）＝f（x）|g（x）|，則函數(shù)h（x）的值域?yàn)镽C．若h（x）＝|f（x）|－|g（x）|，則函數(shù)h（x）有且僅有一個(gè)零點(diǎn)D．若h（x）＝|f（x）|－|g（x）|，則|h（x）|≤4恒成立三、填空題13．（2022·全國(guó)·高三專題練習(xí)）已知偶函數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若函數(shù)SKIPIF1<0恰有4個(gè)不同的零點(diǎn)，則實(shí)數(shù)SKIPIF1<0的取值范圍為_(kāi)_________14．（2020·上?！じ呷龑ｎ}練習(xí)）已知函數(shù)f(x)＝logax＋x－b(a＞0，且a≠1)．當(dāng)2＜a＜3＜b＜4時(shí)，函數(shù)f(x)的零點(diǎn)為x0∈(n，n＋1)，n∈N*，則n=.15．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0SKIPIF1<0.若SKIPIF1<0存在2個(gè)零點(diǎn)，則SKIPIF1<0的取值范圍是__________16．（2022·全國(guó)·高三專題練習(xí)）已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則方程SKIPIF1<0在SKIPIF1<0內(nèi)的所有根之和為_(kāi)_________.四、解答題17．（2014·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0．（1）作出函數(shù)SKIPIF1<0的圖象；（2）若SKIPIF1<0，且SKIPIF1<0，求證：SKIPIF1<0．18．（2022·廣東·東莞市東華高級(jí)中學(xué)高三階段練習(xí)）已知三個(gè)函數(shù)①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0．(1)請(qǐng)從上述三個(gè)函數(shù)中選擇一個(gè)函數(shù)，根據(jù)你選擇的函數(shù)畫(huà)出該函數(shù)的圖象（不用寫(xiě)作圖過(guò)程），并寫(xiě)出該函數(shù)的單調(diào)遞減區(qū)間(不必說(shuō)明理由)；(2)把（1）中所選的函數(shù)記為函數(shù)SKIPIF1<0，若關(guān)于x的方程SKIPIF1<0有且僅有兩個(gè)不同的根，求實(shí)數(shù)k的取值范圍；(3)（請(qǐng)從下面三個(gè)選項(xiàng)中選一個(gè)作答）（i）若（1）中所選①的函數(shù)時(shí)，有SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的值；（ii）若（1）中所選②的函數(shù)時(shí)，有SKIPIF1<0，且SKIPIF1<0，求SKIPIF1<0的取值范圍；（iii）若（1）中所選③的函數(shù)時(shí)，有SKIPIF1<0，且SKIPIF1<0