高考函數(shù)題目及答案

一、單項選擇題（每題2分，共10題）1.函數(shù)f(x)=x^3-ax+1在x=1處取得極值，則a的值為A.3B.-3C.2D.-2答案：A2.函數(shù)f(x)=|x-1|+|x+2|的最小值為A.1B.2C.3D.4答案：B3.函數(shù)f(x)=sin(x)+cos(x)的值域為A.[-√2,√2]B.[-1,1]C.[-√2,1]D.[0,√2]答案：A4.函數(shù)f(x)=e^x-x在R上的單調(diào)性為A.單調(diào)遞增B.單調(diào)遞減C.先增后減D.先減后增答案：A5.函數(shù)f(x)=log_a(x)在x>1時單調(diào)遞增，則a的取值范圍是A.a>1B.0<a<1C.a>0且a≠1D.a<0答案：A6.函數(shù)f(x)=tan(x)在(-π/2,π/2)內(nèi)的圖像是A.單調(diào)遞增B.單調(diào)遞減C.周期函數(shù)D.無界函數(shù)答案：A7.函數(shù)f(x)=x^2-4x+3的圖像是A.拋物線開口向上，頂點(2,-1)B.拋物線開口向下，頂點(2,-1)C.拋物線開口向上，頂點(-2,1)D.拋物線開口向下，頂點(-2,1)答案：A8.函數(shù)f(x)=sin(x)cos(x)的周期為A.πB.2πC.π/2D.4π答案：C9.函數(shù)f(x)=1/x在x>0時的圖像是A.單調(diào)遞增B.單調(diào)遞減C.周期函數(shù)D.無界函數(shù)答案：B10.函數(shù)f(x)=x^3-3x+2的零點個數(shù)為A.1B.2C.3D.0答案：C二、多項選擇題（每題2分，共10題）1.下列函數(shù)中，在x=0處取得極值的有A.f(x)=x^2B.f(x)=x^3C.f(x)=x^4D.f(x)=x^5答案：A,C2.函數(shù)f(x)=|x|在x=0處的導數(shù)為A.0B.1C.-1D.不存在答案：D3.函數(shù)f(x)=sin(x)+cos(x)的導數(shù)為A.cos(x)-sin(x)B.sin(x)+cos(x)C.-sin(x)-cos(x)D.cos(x)+sin(x)答案：A,D4.函數(shù)f(x)=e^x在x=0處的泰勒展開式的前三項為A.1+x+x^2/2B.1-x+x^2/2C.1+x-x^2/2D.1-x-x^2/2答案：A5.函數(shù)f(x)=log(x)在x>1時的導數(shù)為A.1/xB.-1/xC.log(x)D.0答案：A6.函數(shù)f(x)=tan(x)在x=π/4處的導數(shù)為A.1B.-1C.√2D.-√2答案：C7.函數(shù)f(x)=x^2-4x+3的圖像與x軸的交點為A.(1,0)B.(3,0)C.(0,3)D.(0,-3)答案：A,B8.函數(shù)f(x)=sin(x)cos(x)的圖像在x=π/4時的值為A.1/2B.√2/2C.1D.0答案：A9.函數(shù)f(x)=1/x在x=1時的導數(shù)為A.1B.-1C.1/x^2D.-1/x^2答案：C10.函數(shù)f(x)=x^3-3x+2的圖像在x=1處的切線斜率為A.0B.1C.-1D.3答案：C三、判斷題（每題2分，共10題）1.函數(shù)f(x)=x^2在x=0處取得極小值。答案：正確2.函數(shù)f(x)=sin(x)cos(x)的周期為π。答案：正確3.函數(shù)f(x)=e^x在R上單調(diào)遞增。答案：正確4.函數(shù)f(x)=log_a(x)在a>1時單調(diào)遞增。答案：正確5.函數(shù)f(x)=tan(x)在(-π/2,π/2)內(nèi)單調(diào)遞增。答案：正確6.函數(shù)f(x)=x^2-4x+3的圖像是拋物線開口向上。答案：正確7.函數(shù)f(x)=sin(x)cos(x)的周期為2π。答案：錯誤8.函數(shù)f(x)=1/x在x>0時單調(diào)遞減。答案：正確9.函數(shù)f(x)=x^3-3x+2的零點個數(shù)為2。答案：錯誤10.函數(shù)f(x)=log(x)在x>1時的導數(shù)為1/x。答案：正確四、簡答題（每題5分，共4題）1.函數(shù)f(x)=x^3-ax+1在x=1處取得極值，求a的值。答案：f'(x)=3x^2-a，令f'(1)=0，得3-a=0，解得a=3。2.函數(shù)f(x)=|x-1|+|x+2|的最小值。答案：f(x)在x=-2時取得最小值3。3.函數(shù)f(x)=sin(x)+cos(x)的值域。答案：f(x)=√2sin(x+π/4)，值域為[-√2,√2]。4.函數(shù)f(x)=e^x-x在R上的單調(diào)性。答案：f'(x)=e^x-1，當x>0時，f'(x)>0，函數(shù)單調(diào)遞增；當x<0時，f'(x)<0，函數(shù)單調(diào)遞減。五、討論題（每題5分，共4題）1.討論函數(shù)f(x)=x^3-3x+2的單調(diào)性和極值。答案：f'(x)=3x^2-3，令f'(x)=0，得x=±1，當x<-1或x>1時，f'(x)>0，函數(shù)單調(diào)遞增；當-1<x<1時，f'(x)<0，函數(shù)單調(diào)遞減。在x=-1處取得極大值4，在x=1處取得極小值0。2.討論函數(shù)f(x)=sin(x)cos(x)的周期性和單調(diào)性。答案：f(x)=1/2sin(2x)，周期為π，在(0,π/2)內(nèi)單調(diào)遞增，在(π/2,π)內(nèi)單調(diào)遞減。3.討論函數(shù)f(x)=