新高考數(shù)學(xué)一輪復(fù)習(xí)提升訓(xùn)練3.5 冪函數(shù)與一元二次函數(shù)（精講）（原卷版）

3.5冪函數(shù)與一元二次函數(shù)（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點呈現(xiàn)考點呈現(xiàn)例題剖析例題剖析考點一冪函數(shù)及性質(zhì)【例1-1】（2022·全國·高三專題練習(xí)）冪函數(shù)SKIPIF1<0是偶函數(shù)，且在（0，+∞）上是減函數(shù)，則m的值為（

）A．﹣6 B．1 C．6 D．1或﹣6【例1-2】（2022·全國·高三專題練習(xí)）冪函數(shù)SKIPIF1<0是偶函數(shù)，在SKIPIF1<0上是減函數(shù)，則整數(shù)SKIPIF1<0的值為（

）A．0 B．1 C．0或1 D．2【一隅三反】1．（2022·全國·高三專題練習(xí)）（多選）已知冪函數(shù)SKIPIF1<0的圖象經(jīng)過點SKIPIF1<0，則下列說法正確的有（

）A．函數(shù)是偶函數(shù) B．函數(shù)是增函數(shù)C．當(dāng)SKIPIF1<0時，SKIPIF1<0 D．當(dāng)SKIPIF1<0時，SKIPIF1<02．（2022·全國·高三專題練習(xí)）（多選）已知函數(shù)SKIPIF1<0是冪函數(shù)，對任意SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，滿足SKIPIF1<0.若SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0的值為負值，則下列結(jié)論可能成立的有（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<03．（2022·全國·高三專題練習(xí)（理））已知冪函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0軸對稱，與SKIPIF1<0軸及SKIPIF1<0軸均無交點，則由SKIPIF1<0的值構(gòu)成的集合是__________．考點二一元二次函數(shù)【例2-1】（2021·重慶市清華中學(xué)校高三階段練習(xí)）若函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，值域為SKIPIF1<0，則實數(shù)m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·寧夏·平羅中學(xué)模擬預(yù)測（理））已知SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上是增函數(shù)的概率為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-3】（2022·全國·高三專題練習(xí)）（多選）若函數(shù)SKIPIF1<0的定義域為SKIPIF1<0，值域為SKIPIF1<0，則正整數(shù)a的值可能是（

）A．2 B．3 C．4 D．5【一隅三反】1．（2022·全國·高三專題練習(xí)）若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0成等差數(shù)列，則二次函數(shù)SKIPIF1<0的圖象與SKIPIF1<0軸的交點個數(shù)為（

）A．0 B．1 C．2 D．1或22．（2022·天津·南開中學(xué)二模）已知函數(shù)SKIPIF1<0是R上的單調(diào)函數(shù)，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03（2022·重慶·模擬預(yù)測）已知二次函數(shù)SKIPIF1<0的兩個零點都在區(qū)間SKIPIF1<0內(nèi)，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·高三專題練習(xí)（理））若集合SKIPIF1<0中有且只有一個元素，則正實數(shù)SKIPIF1<0的取值范圍是___________考點三一元二次函數(shù)與其他知識綜合【例3】（2022·山東濟寧·三模）已知二次函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2021·廣東·湛江二十一中）若函數(shù)SKIPIF1<0有最大值，則a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·黑龍江）若關(guān)于SKIPIF1<0的方程SKIPIF1<0有解，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考點四圖像問題【例4-1】（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）與函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在同一個坐標(biāo)系內(nèi)的圖象可能是（

）A． B．C． D．【例4-2】（陜西省部分地市學(xué)校2022屆高三下學(xué)期高考全真模擬考試?yán)砜茢?shù)學(xué)試題）函數(shù)SKIPIF1<0的圖象大致是（

）A． B．C． D．【一隅三反】1．（2021·山東·新泰市第一中學(xué)高三階段練習(xí)）若不等式SKIPIF1<0的解集為SKIPIF1<0，則函數(shù)SKIPIF1<0的圖象可以為（

）A． B．C． D．2．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，如果SKIPIF1<0且SKIPIF1<0，則它的圖象可能是（

）A． B．C． D．3．（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0