數(shù)第五單元測(cè)試卷及答案A卷一、選擇題（每題2分，共10分）1.已知函數(shù)f(x)=2x+3，下列說(shuō)法正確的是（）A.函數(shù)f(x)是奇函數(shù)B.函數(shù)f(x)是偶函數(shù)C.函數(shù)f(x)是增函數(shù)D.函數(shù)f(x)是減函數(shù)答案：C2.函數(shù)y=x^2-4x+5的頂點(diǎn)坐標(biāo)是（）A.(2,1)B.(-2,1)C.(2,-1)D.(-2,-1)答案：A3.已知函數(shù)f(x)=x^3-3x+1，下列說(shuō)法正確的是（）A.函數(shù)f(x)在R上單調(diào)遞增B.函數(shù)f(x)在R上單調(diào)遞減C.函數(shù)f(x)在R上先增后減D.函數(shù)f(x)在R上先減后增答案：D4.函數(shù)y=|x|的圖像關(guān)于（）A.x軸對(duì)稱B.y軸對(duì)稱C.原點(diǎn)對(duì)稱D.以上都不對(duì)答案：B5.已知函數(shù)f(x)=x^2-4x+5，下列說(shuō)法正確的是（）A.函數(shù)f(x)的最小值是1B.函數(shù)f(x)的最小值是5C.函數(shù)f(x)的最小值是-1D.函數(shù)f(x)沒有最小值答案：A二、填空題（每題2分，共10分）6.函數(shù)y=x^3+1的導(dǎo)數(shù)是________。答案：3x^27.函數(shù)y=x^2-6x+10的頂點(diǎn)坐標(biāo)是________。答案：(3,1)8.函數(shù)y=|x|+1的值域是________。答案：[1,+∞)9.函數(shù)y=x^2-4x+5的對(duì)稱軸方程是________。答案：x=210.函數(shù)y=x^3-3x+1的極值點(diǎn)是________。答案：x=1三、解答題（每題10分，共30分）11.已知函數(shù)f(x)=x^2-4x+5，求函數(shù)的最小值。解：函數(shù)f(x)=x^2-4x+5=(x-2)^2+1，當(dāng)x=2時(shí)，函數(shù)取得最小值1。12.已知函數(shù)f(x)=x^3-3x+1，求函數(shù)的極值點(diǎn)。解：函數(shù)f(x)的導(dǎo)數(shù)為f'(x)=3x^2-3，令f'(x)=0，解得x=±1。當(dāng)x<-1或x>1時(shí)，f'(x)>0，函數(shù)單調(diào)遞增；當(dāng)-1<x<1時(shí)，f'(x)<0，函數(shù)單調(diào)遞減。因此，x=-1為極大值點(diǎn)，x=1為極小值點(diǎn)。13.已知函數(shù)f(x)=|x|+1，求函數(shù)的值域。解：當(dāng)x≥0時(shí)，f(x)=x+1≥1；當(dāng)x<0時(shí)，f(x)=-x+1>1。因此，函數(shù)f(x)的值域?yàn)閇1,+∞)。四、綜合題（每題15分，共40分）14.已知函數(shù)f(x)=x^3-3x+1，求函數(shù)的單調(diào)區(qū)間和極值。解：函數(shù)f(x)的導(dǎo)數(shù)為f'(x)=3x^2-3，令f'(x)=0，解得x=±1。當(dāng)x<-1或x>1時(shí)，f'(x)>0，函數(shù)單調(diào)遞增；當(dāng)-1<x<1時(shí)，f'(x)<0，函數(shù)單調(diào)遞減。因此，函數(shù)f(x)在(-∞,-1)和(1,+∞)上單調(diào)遞增，在(-1,1)上單調(diào)遞減。當(dāng)x=-1時(shí)，函數(shù)取得極大值f(-1)=3；當(dāng)x=1時(shí)，函數(shù)取得極小值f(1)=-1。15.已知函數(shù)f(x)=x^2-4x+5，求函數(shù)的頂點(diǎn)坐標(biāo)和對(duì)稱軸方程。解：函數(shù)f(x)=x^2-4x+5=