冪函數(shù)與二次函數(shù)題目

二次函數(shù)與冪函數(shù)1.已知冪函數(shù)f(x)=xα的圖象經(jīng)過(guò)點(diǎn)(2,4),則α= ()A.2 B.2C.4 D.82.如果一元二次函數(shù)y=2x2+mx-3的圖象的對(duì)稱軸方程是x=12,那么當(dāng)x=1時(shí),y= (A.-7 B.-5C.-3 D.-13.函數(shù)f(x)=x-12x在區(qū)間(0,+∞)上 (A.有最大值,無(wú)最小值B.有最大值,有最小值C.無(wú)最大值,無(wú)最小值D.無(wú)最大值,有最小值4.[2023·北京海淀區(qū)一模]已知二次函數(shù)f(x),對(duì)任意的x∈R,都有f(2x)<2f(x),則f(x)的大致圖象可能是 () A B C D5.已知冪函數(shù)f(x)=(m2-3)x-m在(0,+∞)上單調(diào)遞增,則實(shí)數(shù)m的值為.

6.設(shè)函數(shù)f(x)=lgx2-ax+12在(1,+∞)上單調(diào)遞增7.設(shè)a=4512,b=5415,c=3434,則A.c<a<b B.c<b<aC.a<c<b D.b<c<a8.[2023·全國(guó)甲卷]已知函數(shù)f(x)=e-(x-1)2,記a=f22,b=f32A.b>c>a B.b>a>cC.c>b>a D.c>a>b9.[2023·無(wú)錫期末]已知函數(shù)f(x)=x2+3,若存在區(qū)間[a,b]?(0,+∞),使得f(x)在[a,b]上的取值范圍為[k(a+1),k(b+1)],則實(shí)數(shù)k的取值范圍為 ()A.(0,3) B.[2,+∞)C.(2,3] D.(2,3)10.若二次函數(shù)f(x)=x2+bx+c滿足:①y=f(x-1)是偶函數(shù);②其圖象截x軸所得的弦長(zhǎng)為2;③其圖象與函數(shù)g(x)=m|x|的圖象有兩個(gè)不同的交點(diǎn).則實(shí)數(shù)m的取值范圍是 ()A.(-∞,-2) B.[0,2)C.(-2,2) D.(-2,2]11.(多選題)已知A(x1,y1),B(x2,y2)(x1<x2)是冪函數(shù)f(x)=x12圖象上的任意兩點(diǎn),則以下結(jié)論正確的是 (A.x1f(x1)<x2f(x2)B.f(x1)x1<f(C.f(xD.fx1+12.函數(shù)f(x)=|x2-3x+2|的單調(diào)遞減區(qū)間是.

13.[2023·遼寧葫蘆島二模]已知函數(shù)f(x)=x2-3x,x≤3,13x-1,14.已知函數(shù)f(x)=|ax-2|x+3(a∈R).(1)當(dāng)a=1時(shí),畫出函數(shù)y=f(x)的圖象;(2)當(dāng)x>0時(shí),f(x)>x恒成立,求a的取值范圍.15.已知二次函數(shù)y=ax2+bx+2(a,b為實(shí)數(shù)).(1)若函數(shù)圖象過(guò)點(diǎn)(1,1),對(duì)任意x∈R,y>0恒成立,求實(shí)數(shù)a的取值范圍;(2)若函數(shù)圖象過(guò)點(diǎn)(1,1),對(duì)任意a∈[-2,-1],y>0恒成立,求實(shí)數(shù)x的取值范圍;(3)對(duì)任意x∈R,b>0時(shí),y≥0恒成立,求a+2b16.[2023·石家莊部分重點(diǎn)高中月考]已知函數(shù)f(x)=4x4-6tx3+(2t2+6)x2-3tx+1(x>0),若f(x)的最小值為0,則t= ()A.2 B.3C.423 D.17.(多選題)已知函數(shù)f(x)=x2+