新高考數(shù)學(xué)一輪復(fù)習(xí)講練測(cè)第2章第03講 冪函數(shù)與二次函數(shù)（練習(xí)）（原卷版）

第03講冪函數(shù)與二次函數(shù)（模擬精練+真題演練）1．（2023·新疆阿勒泰·統(tǒng)考三模）已知函數(shù)則函數(shù)SKIPIF1<0，則函數(shù)SKIPIF1<0的圖象大致是（

）A． B．C． D．2．（2023·湖南婁底·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023·海南·模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的圖象如圖所示，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023·廣東肇慶·?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0，若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<05．（2023·北京海淀·一模）設(shè)SKIPIF1<0，二次函數(shù)SKIPIF1<0的圖象為下列之一，則SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·河南新鄉(xiāng)·高三校聯(lián)考開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0若SKIPIF1<0的最小值為6，則實(shí)數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·全國(guó)·模擬預(yù)測(cè)）已知x，SKIPIF1<0，滿足SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0（

）A．-1 B．0 C．1 D．28．（2023·貴州畢節(jié)·統(tǒng)考二模）已知SKIPIF1<0，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（多選題）（2023·江蘇·校聯(lián)考模擬預(yù)測(cè)）若函數(shù)SKIPIF1<0，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．（多選題）（2023·吉林長(zhǎng)春·東北師大附中校考模擬預(yù)測(cè)）已知冪函數(shù)SKIPIF1<0圖像經(jīng)過(guò)點(diǎn)SKIPIF1<0，則下列命題正確的有（

）A．函數(shù)SKIPIF1<0為增函數(shù) B．函數(shù)SKIPIF1<0為偶函數(shù)C．若SKIPIF1<0，則SKIPIF1<0 D．若SKIPIF1<0，則SKIPIF1<011．（多選題）（2023·全國(guó)·高三專題練習(xí)）已知關(guān)于x的方程x2＋(m－3)x＋m＝0，下列結(jié)論正確的是（

）A．方程x2＋(m－3)x＋m＝0有實(shí)數(shù)根的充要條件是m∈{m|m<1或m>9}B．方程x2＋(m－3)x＋m＝0有一正一負(fù)根的充要條件是m∈{m|m<0}C．方程x2＋(m－3)x＋m＝0有兩正實(shí)數(shù)根的充要條件是m∈{m|0<m≤1}D．方程x2＋(m－3)x＋m＝0無(wú)實(shí)數(shù)根的必要條件是m∈{m|m>1}12．（多選題）（2023·湖南衡陽(yáng)·?？寄M預(yù)測(cè)）設(shè)二次函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，下列各值（或式子）中一定大于SKIPIF1<0的有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0SKIPIF1<0 D．SKIPIF1<0SKIPIF1<013．（2023·上海閔行·統(tǒng)考一模）已知二次函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則函數(shù)SKIPIF1<0的值域?yàn)開(kāi)_____．14．（2023·貴州畢節(jié)·統(tǒng)考模擬預(yù)測(cè)）寫(xiě)出一個(gè)同時(shí)具有下列性質(zhì)①②③的非常值函數(shù)SKIPIF1<0______.①SKIPIF1<0在SKIPIF1<0上恒成立；②SKIPIF1<0是偶函數(shù)；③SKIPIF1<0.15．（2023·陜西西安·西安中學(xué)?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0且SKIPIF1<0的圖象經(jīng)過(guò)定點(diǎn)SKIPIF1<0，若冪函數(shù)SKIPIF1<0的圖象也經(jīng)過(guò)該點(diǎn)，則SKIPIF1<0_______________________．16．（2023·新疆阿克蘇·校考一模）已知二次函數(shù)SKIPIF1<0（a，b為常數(shù)）滿足SKIPIF1<0，且方程SKIPIF1<0有兩等根，SKIPIF1<0在SKIPIF1<0上的最大值為SKIPIF1<0，則SKIPIF1<0的最大值為_(kāi)_________.17．（2023·高三課時(shí)練習(xí)）已知SKIPIF1<0是一元二次方程SKIPIF1<0的兩個(gè)實(shí)數(shù)根.(1)是否存在實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立？若存在，求出SKIPIF1<0的值；若不存在，請(qǐng)說(shuō)明理由；(2)求使SKIPIF1<0的值為整數(shù)的實(shí)數(shù)SKIPIF1<0的整數(shù)值.18．（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，且函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0.（1）求實(shí)數(shù)a的值；（2）若關(guān)于x的不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實(shí)數(shù)m的取值范圍；（3）若關(guān)于x的方程SKIPIF1<0有三個(gè)不同的實(shí)數(shù)根，求實(shí)數(shù)k的取值范圍.19．（2023·高三課時(shí)練習(xí)）已知冪函數(shù)SKIPIF1<0（m為正整數(shù)）的圖像關(guān)于y軸對(duì)稱，且在SKIPIF1<0上是嚴(yán)格減函數(shù)，求滿足SKIPIF1<0的實(shí)數(shù)a的取值范圍．20．（2023·江西鷹潭·高三貴溪市實(shí)驗(yàn)中學(xué)校考階段練習(xí)）已知冪函數(shù)SKIPIF1<0的定義域?yàn)镽.(1)求實(shí)數(shù)SKIPIF1<0的值；(2)若函數(shù)SKIPIF1<0在SKIPIF1<0上不單調(diào)，求實(shí)數(shù)SKIPIF1<0的取值范圍.21．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0在區(qū)間SKIPIF1<0上的值域?yàn)镾KIPIF1<0.(1)求實(shí)數(shù)SKIPIF1<0的值；(2)若不等式SKIPIF1<0

當(dāng)SKIPIF1<0上恒成立，求實(shí)數(shù)k的取值范圍.22．（2023·湖南長(zhǎng)沙·高三校聯(lián)考期中）已知函數(shù)SKIPIF1<0SKIPIF1<0在區(qū)間SKIPIF1<0上有最大值2和最小值1.(1)求SKIPIF1<0的值；(2)不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍；(3)若SKIPIF1<0且方程SKIPIF1<0有三個(gè)不同的實(shí)數(shù)解，求實(shí)數(shù)SKIPIF1<0的取值范圍.1．（2013·浙江·高考真題）已知a，b，c∈R，函數(shù)f(x)＝ax2＋bx＋c.若f(0)＝f（4）>f（1），則（

）A．a(chǎn)>0，4a＋b＝0 B．a(chǎn)<0，4a＋b＝0C．a(chǎn)>0，2a＋b＝0 D．a(chǎn)<0，2a＋b＝02．（2016·浙江·高考真題）已知函數(shù)SKIPIF1<0，則“b＜0”是“SKIPIF1<0的最小值與f(x)的最小值相等”的A．充分不必要條件 B．必要不充分條件C．充分必要條件 D．既不充分也不必要條件3．（2015·四川·高考真題）如果函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則mn的最大值為A．16 B．18 C．25 D．SKIPIF1<04．（2015·陜西·高考真題）對(duì)二次函數(shù)SKIPIF1<0（SKIPIF1<0為非零整數(shù)），四位同學(xué)分別給出下列結(jié)論，其中有且僅有一個(gè)結(jié)論是錯(cuò)誤的，則錯(cuò)誤的結(jié)論是（）A．SKIPIF1<0是SKIPIF1<0的零點(diǎn) B．1是SKIPIF1<0的極值點(diǎn)C．3是SKIPIF1<0的極值 D．點(diǎn)SKIPIF1<0在曲線SKIPIF1<0上5．（2015·湖北·高考真題）SKIPIF1<0為實(shí)數(shù)，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值記為SKIPIF1<0.當(dāng)SKIPIF1<0_________時(shí)，SKIPIF1<0的值最小.6．（2015·浙江·高考真題）已知函數(shù)SKIPIF1<0，記SKIPIF1<0是SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值.（1）證明：當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；（2）當(dāng)SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，求SK