課時規(guī)范練13函數(shù)圖象高考總復(fù)習(xí)優(yōu)化設(shè)計GAOKAOZONGFUXIYOUHUASHEJI2026基礎(chǔ)鞏固練1234567891011121314151617

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12345678910111213141516174.(2024·陜西西安模擬)已知函數(shù)f(x)在區(qū)間[-2,2]上的大致圖象如圖所示,則f(x)的解析式可以是(

)A.f(x)=(ex-e-x)x B.f(x)=(ex-e-x)sinxC.f(x)=(ex-e-x)cosx D.f(x)=(ex-e-x)x2C1234567891011121314151617

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AB1234567891011121314151617解析

作出函數(shù)圖象(如圖所示),顯然圖象不關(guān)于原點中心對稱,故A錯誤;f(x)圖象與直線y=1有一個交點,故B錯誤;由圖象知函數(shù)的值域為[0,+∞),且在區(qū)間(-∞,0)內(nèi)單調(diào)遞增,故C,D正確.故選AB.1234567891011121314151617

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<12345678910111213141516179.(2024·山東濰坊模擬)設(shè)0<a<b,若函數(shù)y=|log2x-1|,x∈[a,b]的值域為[0,1],則a+b的取值范圍是(

)A.(3,6) B.[3,6]C.(4,5) D.[4,5]綜合提升練B1234567891011121314151617解析

作出函數(shù)圖象(如圖所示),由f(x)=0,得x=2,由f(x)=1,得x=1或x=4,又因為0<a<b.①若a>2,則不合題意,舍去;②若a=2,則b=4,此時a+b=6;③若1<a<2,則b=4,此時5<a+b<6;④若a=1,則2≤b≤4,3≤a+b≤5.綜上,3≤a+b≤6.1234567891011121314151617

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123456789101112131415161711.(多選題)已知a,b分別是方程2x+x=0,3x+x=0的實數(shù)根,則下列關(guān)系式中正確的是(

)A.-1<b<a<0 B.-1<a<b<0C.b·3a<a·3b

D.a·2b<b·2aBD解析

函數(shù)y=2x,y=3x,y=-x在同一坐標(biāo)系中的圖象如圖,所以-1<a<b<0,所以2a<2b,3a<3b,0<-b<-a,所以-b·2a<(-a)·2b,-b·3a<(-a)·3b,所以a·2b<b·2a,a·3b<b·3a.故選BD.123456789101112131415161712.(多選題)已知f(x)是定義在R上的偶函數(shù),且對?x∈R,有f(1-x)=-f(1+x),當(dāng)x∈[0,1]時,f(x)=x2+x-2,則(

)A.f(x)的周期是2B.點(-3,0)是函數(shù)f(x)圖象的一個對稱中心C.f(2024)+f(2025)=-2D.函數(shù)y=f(x)-log2(x+1)有3個零點BCD1234567891011121314151617

123456789101112131415161713.(2024·廣西柳州模擬)記實數(shù)x1,x2,…,xn的最小數(shù)為min{x1,x2,…,xn},若f(x)=min{x+1,x2-2x+1,-x+8},則函數(shù)f(x)的最大值為

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1234567891011121314151617創(chuàng)新應(yīng)用練

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1234567891011121314151617對于C項,由A,B可知,當(dāng)x∈[0,1)時,f(x)=-21-x,且f(x)的周期為2.又當(dāng)-1≤x<0時,f(x)=2x,作出函數(shù)y=f(x)以及y=g(x)的圖象如圖所示.顯然,當(dāng)x<2時,f(x)的圖象與g(x)=log0.5x的圖象沒有交點.又f(4)=f(2)=f(0)=-2,g(2)=log0.52=-1,g(4)=