高中函數(shù)大題題目及答案

一、單項(xiàng)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.3C.0D.2答案：B3.函數(shù)f(x)=e^x-x在區(qū)間(-∞,+∞)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：A4.函數(shù)f(x)=sin(x)+cos(x)的周期為A.πB.2πC.π/2D.4π答案：B5.函數(shù)f(x)=log_a(x)在x>1時(shí)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)=x^2-4x+3的圖像與x軸的交點(diǎn)個(gè)數(shù)為A.0B.1C.2D.3答案：C7.函數(shù)f(x)=tan(x)在區(qū)間(-π/2,π/2)內(nèi)的值域?yàn)锳.(-∞,+∞)B.[0,+∞)C.(-1,1)D.R答案：A8.函數(shù)f(x)=x^3-3x+1的極值點(diǎn)個(gè)數(shù)為A.0B.1C.2D.3答案：C9.函數(shù)f(x)=arctan(x)+arccot(x)的值為A.π/2B.πC.0D.-π/2答案：A10.函數(shù)f(x)=x^2-2x+3的頂點(diǎn)坐標(biāo)為A.(1,2)B.(1,3)C.(-1,2)D.(-1,3)答案：B二、多項(xiàng)選擇題（每題2分，共10題）1.函數(shù)f(x)=x^3-3x+2的圖像具有以下性質(zhì)A.對(duì)稱(chēng)軸為x=0B.有兩個(gè)零點(diǎn)C.在(-∞,1)上單調(diào)遞減D.在(1,+∞)上單調(diào)遞增答案：BCD2.函數(shù)f(x)=|x|在區(qū)間[-1,1]上的最小值為A.-1B.0C.1D.2答案：B3.函數(shù)f(x)=sin(x)cos(x)的周期為A.πB.2πC.π/2D.4π答案：A4.函數(shù)f(x)=e^x在區(qū)間(-∞,+∞)上的圖像特征為A.過(guò)點(diǎn)(0,1)B.單調(diào)遞增C.無(wú)界D.有漸近線答案：ABC5.函數(shù)f(x)=log_2(x)在x>1時(shí)單調(diào)遞增，則f(x)的圖像特征為A.過(guò)點(diǎn)(1,0)B.單調(diào)遞增C.無(wú)界D.有漸近線答案：ABD6.函數(shù)f(x)=x^2-4x+4的圖像與x軸的交點(diǎn)個(gè)數(shù)為A.0B.1C.2D.3答案：B7.函數(shù)f(x)=tan(x)在區(qū)間(-π/2,π/2)內(nèi)的值域?yàn)锳.(-∞,+∞)B.[0,+∞)C.(-1,1)D.R答案：AD8.函數(shù)f(x)=x^3-3x+1的極值點(diǎn)個(gè)數(shù)為A.0B.1C.2D.3答案：C9.函數(shù)f(x)=arctan(x)+arccot(x)的值為A.π/2B.πC.0D.-π/2答案：A10.函數(shù)f(x)=x^2-2x+3的頂點(diǎn)坐標(biāo)為A.(1,2)B.(1,3)C.(-1,2)D.(-1,3)答案：B三、判斷題（每題2分，共10題）1.函數(shù)f(x)=x^2在區(qū)間(-1,1)上單調(diào)遞增正確2.函數(shù)f(x)=sin(x)+cos(x)的周期為π錯(cuò)誤3.函數(shù)f(x)=e^x-x在區(qū)間(-∞,+∞)上單調(diào)遞增正確4.函數(shù)f(x)=log_a(x)在x>1時(shí)單調(diào)遞增，則a>1正確5.函數(shù)f(x)=x^2-4x+3的圖像與x軸的交點(diǎn)個(gè)數(shù)為2正確6.函數(shù)f(x)=tan(x)在區(qū)間(-π/2,π/2)內(nèi)的值域?yàn)?-∞,+∞)正確7.函數(shù)f(x)=x^3-3x+1的極值點(diǎn)個(gè)數(shù)為2正確8.函數(shù)f(x)=arctan(x)+arccot(x)的值為π/2正確9.函數(shù)f(x)=x^2-2x+3的頂點(diǎn)坐標(biāo)為(1,2)錯(cuò)誤10.函數(shù)f(x)=x^2-2x+3的頂點(diǎn)坐標(biāo)為(1,3)正確四、簡(jiǎn)答題（每題5分，共4題）1.函數(shù)f(x)=x^3-3x+2的圖像具有哪些性質(zhì)？答案：函數(shù)f(x)=x^3-3x+2的圖像具有以下性質(zhì)：對(duì)稱(chēng)軸為x=1，有兩個(gè)零點(diǎn)，在(-∞,1)上單調(diào)遞減，在(1,+∞)上單調(diào)遞增。2.函數(shù)f(x)=sin(x)cos(x)的圖像具有哪些特征？答案：函數(shù)f(x)=sin(x)cos(x)的圖像具有以下特征：周期為π，圖像在x軸上對(duì)稱(chēng)，圖像在(0,π/2)和(π,3π/2)上單調(diào)遞增，在(π/2,π)和(3π/2,2π)上單調(diào)遞減。3.函數(shù)f(x)=e^x在區(qū)間(-∞,+∞)上的圖像特征是什么？答案：函數(shù)f(x)=e^x在區(qū)間(-∞,+∞)上的圖像特征為：過(guò)點(diǎn)(0,1)，單調(diào)遞增，無(wú)界，有漸近線x=-∞。4.函數(shù)f(x)=log_2(x)在x>1時(shí)單調(diào)遞增，則f(x)的圖像特征是什么？答案：函數(shù)f(x)=log_2(x)在x>1時(shí)單調(diào)遞增，則f(x)的圖像特征為：過(guò)點(diǎn)(1,0)，單調(diào)遞增，無(wú)界，有漸近線x=0。五、討論題（每題5分，共4題）1.函數(shù)f(x)=x^3-3x+2的圖像與x軸的交點(diǎn)有哪些？答案：函數(shù)f(x)=x^3-3x+2的圖像與x軸的交點(diǎn)為x=-2，x=1?？梢酝ㄟ^(guò)求解方程x^3-3x+2=0得到這些交點(diǎn)。2.函數(shù)f(x)=sin(x)cos(x)的周期是多少？如何確定？答案：函數(shù)f(x)=sin(x)cos(x)的周期為π。可以通過(guò)觀察函數(shù)的圖像或者利用三角恒等式sin(2x)=2sin(x)cos(x)來(lái)確定周期。3.函數(shù)f(x)=e^x在區(qū)間(-∞,+∞)上的圖像特征是什么？如何描述？答案：函數(shù)f(x)=e^x在區(qū)間(-∞,+∞)上的圖像特征為：過(guò)點(diǎn)(0,1)，單調(diào)遞增，無(wú)界，有漸近線x=-∞?？梢酝ㄟ^(guò)觀察函數(shù)的圖像或者利用導(dǎo)數(shù)來(lái)描述這些特征。4.函數(shù)f(x)