2022高考數(shù)學(xué)一輪復(fù)習(xí)課時(shí)規(guī)范練8冪函數(shù)與二次函數(shù)文含解析新人教A版

1、課時(shí)規(guī)范練8冪函數(shù)與二次函數(shù)基礎(chǔ)鞏固組1.冪函數(shù)y=f(x)經(jīng)過(guò)點(diǎn)(3,3),則f(x)是()a.偶函數(shù),且在(0,+)上是增函數(shù)b.偶函數(shù),且在(0,+)上是減函數(shù)c.奇函數(shù),且在(0,+)上是減函數(shù)d.非奇非偶函數(shù),且在(0,+)上是增函數(shù)2.若函數(shù)y=x2-3x-4的定義域?yàn)?,m,值域?yàn)?254,-4,則m的取值范圍是()a.0,4b.32,4c.32,+d.32,33.二次函數(shù)f(x)的圖象如圖所示,則f(x-1)0的解集為()a.(-2,1)b.(0,3)c.(-1,2d.(-,0)(3,+)4.(2020廣東鹽田二模,6)關(guān)于x的方程ax2+(1-a)x-1=0,下列結(jié)論正確的是

2、()a.當(dāng)a=0時(shí),方程無(wú)實(shí)數(shù)根b.當(dāng)a=-1時(shí),方程只有一個(gè)實(shí)數(shù)根c.當(dāng)a=1時(shí),方程有兩個(gè)不相等的實(shí)數(shù)根d.當(dāng)a0時(shí),方程有兩個(gè)相等的實(shí)數(shù)根5.(2020福建三明模擬,理7)已知函數(shù)f(x)=mx2+(m-3)x+1的圖象與x軸的交點(diǎn)中至少有一個(gè)在原點(diǎn)右側(cè),則實(shí)數(shù)m的取值范圍是()a.0,1b.(0,1)c.(-,1)d.(-,16.已知點(diǎn)(m,8)在冪函數(shù)f(x)=(m-1)xn的圖象上,設(shè)a=f1312,b=f(ln ),c=f-12,則a,b,c的大小關(guān)系為()a.cabb.abcc.bcad.ba0),已知f(m)0d.f(m+1)0的解集為x|-1x0的解集為(0,3).故選b.

3、4.c當(dāng)a=0時(shí),方程為x-1=0,即x=1,故選項(xiàng)a錯(cuò)誤;當(dāng)a=-1時(shí),方程變?yōu)?x2+2x-1=0,因?yàn)?4-4=0,所以方程有兩個(gè)相等的實(shí)數(shù)根,故選項(xiàng)b錯(cuò)誤;當(dāng)a=1時(shí),方程變?yōu)閤2-1=0,得x=1,故選項(xiàng)c正確;當(dāng)a0時(shí),=(1-a)2+4a=(1+a)20,所以方程有兩個(gè)實(shí)數(shù)根,故選項(xiàng)d錯(cuò)誤,所以選c.5.d當(dāng)m=0,令f(x)=0得,-3x+1=0,得x=13,符合題意;當(dāng)m0時(shí),由f(0)=1可知,若滿足題意,則需(m-3)2-4m0,-m-32m0,得0m1;當(dāng)m0時(shí),由f(0)=1可知,函數(shù)f(x)的圖象恒與x軸的正半軸有一個(gè)交點(diǎn).綜上可知,m的取值范圍是(-,1.故選d.

4、6.a根據(jù)題意,m-1=1,m=2,2n=8,n=3,f(x)=x3.f(x)=x3是定義在r上的增函數(shù),又-1201312130=1ln ,ca0,由f(m)0,得-1m0,0m+1-12時(shí),函數(shù)f(x)單調(diào)遞增,f(m+1)f(0)0f(m).(方法2)因?yàn)閒(x)圖象的對(duì)稱軸為x=-12,f(0)=a0,所以f(x)的大致圖象如圖所示.由f(m)0,得-1m0,所以f(m+1)f(0)0.13.(-,1(2,3)對(duì)命題p,因?yàn)閤r,x2+2x+m0,所以4-4m0,解得m1;對(duì)命題q,因?yàn)閮绾瘮?shù)f(x)=x1m-3+1在(0,+)上是減函數(shù),所以1m-3+10,解得2m3.因?yàn)椤皃q”為真命題,“pq”為假命題,所以p,q一真一假.若p真q假,可得m1;若p假q真,可得2m0).令y=lnxx,故可得y=1-lnxx2,令y=0,解得x=e,故易得y=lnxx在(0,e)上單調(diào)遞增,在(e,+)上單調(diào)遞減.故lnxxmax=1e,則a1e.所以若pq為真,則a(-,2,故選d.16.(-,-20,+)由題得二次函數(shù)的對(duì)稱軸為x=-12.因?yàn)楹瘮?shù)|f(x)|在區(qū)間0,1上單調(diào),所以當(dāng)函數(shù)單調(diào)遞增時(shí),=1-4m