新高考數(shù)學一輪復習講練測第2章第03講 冪函數(shù)與二次函數(shù)（練習）（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)考模擬預測）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023·海南·模擬預測）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·校考模擬預測）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則實數(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)考開學考試）已知函數(shù)SKIPIF1<0若SKIPIF1<0的最小值為6，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·全國·模擬預測）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)考模擬預測）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·吉林長春·東北師大附中?？寄M預測）已知冪函數(shù)SKIPIF1<0圖像經(jīng)過點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·高三專題練習）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有一正一負根的充要條件是m∈{m|m<0}C．方程x2＋(m－3)x＋m＝0有兩正實數(shù)根的充要條件是m∈{m|0<m≤1}D．方程x2＋(m－3)x＋m＝0無實數(shù)根的必要條件是m∈{m|m>1}12．（多選題）（2023·湖南衡陽·?？寄M預測）設二次函數(shù)SKIPIF1<0的值域為SKIPIF1<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的值域為SKIPIF1<0，則函數(shù)SKIPIF1<0的值域為______．14．（2023·貴州畢節(jié)·統(tǒng)考模擬預測）寫出一個同時具有下列性質(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?？寄M預測）已知函數(shù)SKIPIF1<0且SKIPIF1<0的圖象經(jīng)過定點SKIPIF1<0，若冪函數(shù)SKIPIF1<0的圖象也經(jīng)過該點，則SKIPIF1<0_______________________．16．（2023·新疆阿克蘇·?？家荒＃┮阎魏瘮?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__________.17．（2023·高三課時練習）已知SKIPIF1<0是一元二次方程SKIPIF1<0的兩個實數(shù)根.(1)是否存在實數(shù)SKIPIF1<0，使得SKIPIF1<0成立？若存在，求出SKIPIF1<0的值；若不存在，請說明理由；(2)求使SKIPIF1<0的值為整數(shù)的實數(shù)SKIPIF1<0的整數(shù)值.18．（2023·全國·高三專題練習）已知函數(shù)SKIPIF1<0，且函數(shù)SKIPIF1<0的值域為SKIPIF1<0.（1）求實數(shù)a的值；（2）若關(guān)于x的不等式SKIPIF1<0在SKIPIF1<0上恒成立，求實數(shù)m的取值范圍；（3）若關(guān)于x的方程SKIPIF1<0有三個不同的實數(shù)根，求實數(shù)k的取值范圍.19．（2023·高三課時練習）已知冪函數(shù)SKIPIF1<0（m為正整數(shù)）的圖像關(guān)于y軸對稱，且在SKIPIF1<0上是嚴格減函數(shù)，求滿足SKIPIF1<0的實數(shù)a的取值范圍．20．（2023·江西鷹潭·高三貴溪市實驗中學?？茧A段練習）已知冪函數(shù)SKIPIF1<0的定義域為R.(1)求實數(shù)SKIPIF1<0的值；(2)若函數(shù)SKIPIF1<0在SKIPIF1<0上不單調(diào)，求實數(shù)SKIPIF1<0的取值范圍.21．（2023·全國·高三專題練習）已知SKIPIF1<0在區(qū)間SKIPIF1<0上的值域為SKIPIF1<0.(1)求實數(shù)SKIPIF1<0的值；(2)若不等式SKIPIF1<0

當SKIPIF1<0上恒成立，求實數(shù)k的取值范圍.22．（2023·湖南長沙·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，求實數(shù)SKIPIF1<0的取值范圍；(3)若SKIPIF1<0且方程SKIPIF1<0有三個不同的實數(shù)解，求實數(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）對二次函數(shù)SKIPIF1<0（SKIPIF1<0為非零整數(shù)），四位同學分別給出下列結(jié)論，其中有且僅有一個結(jié)論是錯誤的，則錯誤的結(jié)論是（）A．SKIPIF1<0是SKIPIF1<0的零點 B．1是SKIPIF1<0的極值點C．3是SKIPIF1<0的極值 D．點SKIPIF1<0在曲線SKIPIF1<0上5．（2015·湖北·高考真題）SKIPIF1<0為實數(shù)，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值記為SKIPIF1<0.當SKIPIF1<0_________時，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SKIPIF1<0時，SKIPIF1<0；（2）當SKIPIF1<0，SKIPIF1<0滿足SKIPIF1<0，求SK