新高考數(shù)學(xué)一輪復(fù)習(xí) 專項(xiàng)分層精練第05課 函數(shù)的單調(diào)性與最值（原卷版）

第02課函數(shù)的單調(diào)性與最值（分層專項(xiàng)精練）【一層練基礎(chǔ)】一、單選題1．（2012·天津·高考真題）下列函數(shù)中，既是偶函數(shù)，又在區(qū)間（1,2）內(nèi)是增函數(shù)的為A．SKIPIF1<0，xSKIPIF1<0RB．SKIPIF1<0，xSKIPIF1<0R且x≠0C．SKIPIF1<0,xSKIPIF1<0RD．SKIPIF1<0，xSKIPIF1<0R2．（2022秋·浙江杭州·高一?？计谥校┖瘮?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<03．（2023·全國·高三專題練習(xí)）設(shè)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．（2020春·山西太原·高二山西大附中?？茧A段練習(xí)）若關(guān)于x的不等式SKIPIF1<0在SKIPIF1<0區(qū)間上有解，則k的取值范圍是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·吉林白城·?？寄M預(yù)測(cè)）若函數(shù)SKIPIF1<0存在平行于SKIPIF1<0軸的切線，則實(shí)數(shù)SKIPIF1<0取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題6．（2021秋·甘肅蘭州·高一蘭州一中?？计谥校┮阎瘮?shù)SKIPIF1<0，則下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0上是增函數(shù)B．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0中心對(duì)稱C．函數(shù)SKIPIF1<0的圖象上存在兩點(diǎn)SKIPIF1<0，SKIPIF1<0，使得直線SKIPIF1<0軸D．函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱7．（2023春·重慶九龍坡·高一四川外國語大學(xué)附屬外國語學(xué)校?？茧A段練習(xí)）設(shè)函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0的一個(gè)周期為SKIPIF1<0 B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．SKIPIF1<0在SKIPIF1<0上有最大值SKIPIF1<0 D．SKIPIF1<0圖象的一條對(duì)稱軸為直線SKIPIF1<08．（2021秋·福建三明·高三?？计谥校┫铝泻瘮?shù)中是偶函數(shù)，且在區(qū)間SKIPIF1<0上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0的定義域?yàn)镾KIPIF1<0 B．SKIPIF1<0是偶函數(shù)C．函數(shù)SKIPIF1<0的零點(diǎn)為0 D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的最大值為SKIPIF1<0三、填空題10．（2022秋·陜西西安·高一西安市第八十三中學(xué)校考階段練習(xí)）函數(shù)SKIPIF1<0的單調(diào)增區(qū)間為．11．（2023春·安徽亳州·高二亳州二中?？计谀┮阎x域?yàn)镾KIPIF1<0的減函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，則不等式SKIPIF1<0的解集為.12．（2016·北京·高考真題）函數(shù)SKIPIF1<0的最大值為.13．（2022秋·天津西青·高一天津市西青區(qū)楊柳青第一中學(xué)校考期中）若兩個(gè)正實(shí)數(shù)x，y滿足SKIPIF1<0，且不等式SKIPIF1<0恒成立，則實(shí)數(shù)m的取值范圍是．14．（2023·全國·高三專題練習(xí)）已知實(shí)數(shù)a，b滿足SKIPIF1<0，則SKIPIF1<0的最小值是.【二層練綜合】一、單選題1．（2022秋·高一單元測(cè)試）已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，且對(duì)任意的SKIPIF1<0，都有SKIPIF1<0SKIPIF1<0，則滿足不等式SKIPIF1<0的SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·全國·高一專題練習(xí)）函數(shù)y＝SKIPIF1<0，x∈(m，n]的最小值為0，則m的取值范圍是（

）A．(1，2) B．(－1，2) C．[1，2) D．[－1，2)3．（2023·四川·模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0且SKIPIF1<0在定義域上是單調(diào)函數(shù)，則實(shí)數(shù)t的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·安徽滁州·高二校考學(xué)業(yè)考試）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，滿足：①對(duì)任意SKIPIF1<0，都有SKIPIF1<0，②對(duì)任意SKIPIF1<0且SKIPIF1<0，都有SKIPIF1<0，則函數(shù)SKIPIF1<0叫“成功函數(shù)”，下列函數(shù)是“成功函數(shù)”的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是定義域?yàn)镾KIPIF1<0的奇函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．若函數(shù)SKIPIF1<0在SKIPIF1<0上的最小值為3，則實(shí)數(shù)a的值為（

）A．1 B．2 C．3 D．4二、多選題6．（2022秋·山東濰坊·高三?？计谥校┫铝兴膫€(gè)函數(shù)中，以SKIPIF1<0為周期且在SKIPIF1<0上單調(diào)遞增的偶函數(shù)有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2023春·湖北恩施·高一校聯(lián)考期中）已知函數(shù)SKIPIF1<0，SKIPIF1<0，則（

）A．函數(shù)SKIPIF1<0為偶函數(shù)B．函數(shù)SKIPIF1<0為奇函數(shù)C．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值與最小值之和為0D．設(shè)SKIPIF1<0，則SKIPIF1<0的解集為SKIPIF1<08．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0，SKIPIF1<0在SKIPIF1<0單調(diào)遞減，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2022·全國·高三專題練習(xí)）高斯是德國著名數(shù)學(xué)家，近代數(shù)學(xué)奠基者之一，享有“數(shù)學(xué)王子”的稱號(hào)，他和阿基米德，牛頓并列為世界三大數(shù)學(xué)家，用SKIPIF1<0表示不超過x的最大整數(shù)，則SKIPIF1<0稱為高斯函數(shù)，例如SKIPIF1<0，SKIPIF1<0.則下列說法正確的是（

）A．函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0（SKIPIF1<0）上單調(diào)遞增B．若函數(shù)SKIPIF1<0，則SKIPIF1<0的值域?yàn)镾KIPIF1<0C．若函數(shù)SKIPIF1<0，則SKIPIF1<0的值域?yàn)镾KIPIF1<0D．SKIPIF1<0，SKIPIF1<0三、填空題10．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上的最小值為1，則SKIPIF1<0的值為.11．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0（x>0），若SKIPIF1<0的最大值為SKIPIF1<0，則正實(shí)數(shù)a=.12．（2022·全國·高三專題練習(xí)）若SKIPIF1<0，SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為.13．（2023·全國·高三專題練習(xí)）若SKIPIF1<0，使SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是．14．（2021秋·湖北荊州·高一荊州市沙市第五中學(xué)?？茧A段練習(xí)）同學(xué)們，你們是否注意到：自然下垂的鐵鏈；空曠的田野上，兩根電線桿之間的電線；峽谷的上空，橫跨深澗的觀光索道的鋼索．這些現(xiàn)象中都有相似的曲線形態(tài)．事實(shí)上，這些曲線在數(shù)學(xué)上常常被稱為懸鏈線．懸鏈線的相關(guān)理論在工程、航海、光學(xué)等方面有廣泛的應(yīng)用．在恰當(dāng)?shù)淖鴺?biāo)系中，這類函數(shù)的表達(dá)式可以為SKIPIF1<0（其中SKIPIF1<0，SKIPIF1<0是非零常數(shù)，無理數(shù)SKIPIF1<0…），對(duì)于函數(shù)SKIPIF1<0以下結(jié)論正確的是．①如果SKIPIF1<0，那么函數(shù)SKIPIF1<0為奇函數(shù)；②如果SKIPIF1<0，那么SKIPIF1<0為單調(diào)函數(shù)；③如果SKIPIF1<0，那么函數(shù)SKIPIF1<0沒有零點(diǎn)；④如果SKIPIF1<0那么函數(shù)SKIPIF1<0的最小值為2．【三層練能力】一、單選題1．（2023·全國·高三專題練習(xí)）已知a，b，c滿足SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<02．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習(xí)）已知關(guān)于SKIPIF1<0的不等式SKIPIF1<0有且僅有兩個(gè)正整數(shù)解（其中SKIPIF1<0為自然對(duì)數(shù)的底數(shù)），則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2023·全國·校聯(lián)考一模）曲線的曲率就是針對(duì)曲線上?個(gè)克的切線方向角對(duì)弧長的轉(zhuǎn)動(dòng)率，表明曲線偏離直線的程度，曲率越大，表示曲線的彎曲程度越大．曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的曲率SKIPIF1<0SKIPIF1<0，其中SKIPIF1<0是SKIPIF1<0的導(dǎo)函數(shù)．（

）A．若函數(shù)f（x）=SKIPIF1<0．則曲線y=f（x）在點(diǎn)（-SKIPIF1<0，-SKIPIF1<0）與點(diǎn)（SKIPIF1<0，SKIPIF1<0）處的彎曲程度相同B．若SKIPIF1<0是二次函數(shù)．則曲線SKIPIF1<0的曲率在頂點(diǎn)處取得最小值C．若函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0D．若函數(shù)SKIPIF1<0