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第09講二次函數(shù)與冪函數(shù)(精練)【A組
】一、單選題1.下列函數(shù)中定義域?yàn)镾KIPIF1<0的是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.已知冪函數(shù)SKIPIF1<0的圖象經(jīng)過(guò)點(diǎn)SKIPIF1<0,則SKIPIF1<0的大致圖象是(
)A. B.C. D.3.設(shè)SKIPIF1<0,則“SKIPIF1<0”是“SKIPIF1<0”的(
)A.充分不必要條件 B.必要不充分條件C.充分必要條件 D.既不充分也不必要條件4.已知函數(shù)SKIPIF1<0是冪函數(shù),且在SKIPIF1<0上遞減,則實(shí)數(shù)SKIPIF1<0(
)A.SKIPIF1<0 B.2或SKIPIF1<0 C.4 D.25.已知函數(shù)SKIPIF1<0是冪函數(shù),則下列關(guān)于SKIPIF1<0說(shuō)法正確的是(
)A.奇函數(shù) B.偶函數(shù) C.定義域?yàn)镾KIPIF1<0 D.在SKIPIF1<0單調(diào)遞減6.SKIPIF1<0的最大值是(
)A.SKIPIF1<0 B.2 C.SKIPIF1<0 D.47.已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是單調(diào)函數(shù),則實(shí)數(shù)k的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.設(shè)SKIPIF1<0是定義在SKIPIF1<0上偶函數(shù),則SKIPIF1<0在區(qū)間SKIPIF1<0上是(
)A.增函數(shù) B.減函數(shù) C.先增后減函數(shù) D.與SKIPIF1<0,SKIPIF1<0有關(guān),不能確定9.冪函數(shù)SKIPIF1<0在R上單調(diào)遞增,則函數(shù)SKIPIF1<0的圖象過(guò)定點(diǎn)(
)A.(1,1) B.(1,2) C.(-3,1) D.(-3,2)二、填空題10.若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)存在最小值,則SKIPIF1<0的取值范圍是___________.11.已知函數(shù)SKIPIF1<0,SKIPIF1<0是嚴(yán)格減函數(shù),則實(shí)數(shù)SKIPIF1<0的取值范圍是______.12.已知函數(shù)SKIPIF1<0,則其值域?yàn)開(kāi)_________.13.已知冪函數(shù)SKIPIF1<0為偶函數(shù),則該函數(shù)的增區(qū)間為_(kāi)______.14.若函數(shù)SKIPIF1<0是冪函數(shù),且SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,則SKIPIF1<0___________.三、解答題15.比較下列各組數(shù)的大小:(1)SKIPIF1<0;(2)SKIPIF1<0,SKIPIF1<0;16.已知冪函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0軸對(duì)稱,且在SKIPIF1<0上是減函數(shù),(1)求SKIPIF1<0的值.(2)若SKIPIF1<0,求SKIPIF1<0的取值范圍.【B組】一、單選題1.下列比較大小中正確的是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.已知冪函數(shù)的圖象經(jīng)過(guò)點(diǎn)SKIPIF1<0,則該冪函數(shù)的大致圖象是(
)A. B.C. D.3.已知冪函數(shù)SKIPIF1<0為偶函數(shù),若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上為單調(diào)函數(shù),則實(shí)數(shù)SKIPIF1<0的取值范圍為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是單調(diào)函數(shù),則實(shí)數(shù)k的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<05.已知冪函數(shù)SKIPIF1<0滿足條件SKIPIF1<0,則實(shí)數(shù)a的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.設(shè)SKIPIF1<0,SKIPIF1<0,函數(shù)SKIPIF1<0,若SKIPIF1<0恒成立,則(
)A.SKIPIF1<0,SKIPIF1<0 B.SKIPIF1<0,SKIPIF1<0C.SKIPIF1<0,SKIPIF1<0 D.SKIPIF1<0,SKIPIF1<0二、多選題7.已知冪函數(shù)SKIPIF1<0,則(
)A.SKIPIF1<0,函數(shù)SKIPIF1<0的圖像與坐標(biāo)軸沒(méi)有交點(diǎn)B.SKIPIF1<0,使得SKIPIF1<0是奇函數(shù)C.當(dāng)SKIPIF1<0時(shí),函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增D.當(dāng)SKIPIF1<0時(shí),函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0三、填空題8.函數(shù)SKIPIF1<0的值域?yàn)開(kāi)_________.9.設(shè)SKIPIF1<0(SKIPIF1<0為常數(shù)),則“函數(shù)SKIPIF1<0的圖象經(jīng)過(guò)點(diǎn)SKIPIF1<0”是“函數(shù)SKIPIF1<0為偶函數(shù)”的____________條件.(填“充分不必要”、“必要不充分”、“充要””、“既不充分也不必要”)10.請(qǐng)寫(xiě)出一個(gè)冪函數(shù)SKIPIF1<0,滿足:SKIPIF1<0,SKIPIF1<0.此函數(shù)可以是SKIPIF1<0______.11.已知函數(shù)SKIPIF1<0,則關(guān)于SKIPIF1<0的表達(dá)式SKIPIF1<0的解集為_(kāi)_________.12.已知函數(shù)SKIPIF1<0(SKIPIF1<0),若函數(shù)SKIPIF1<0在SKIPIF1<0的最小值為SKIPIF1<0,則實(shí)數(shù)SKIPIF1<0的值為_(kāi)_______.13.設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是嚴(yán)格增函數(shù),則實(shí)數(shù)SKIPIF1<0的取值范圍為_(kāi)_________.14.已知函數(shù)SKIPIF1<0,定義SKIPIF1<0,若SKIPIF1<0恒成立,則實(shí)數(shù)SKIPIF1<0的取值范圍是___________.四、解答題15.已知冪函數(shù)SKIPIF1<0是偶函數(shù).(1)求函數(shù)SKIPIF1<0的解析式;(2)若SKIPIF1<0,求x的取值范圍.16.已知冪函數(shù)SKIPIF1<0為偶函數(shù),SKIPIF1<0.(1)若SKIPIF1<0,求SKIPIF1<0;(2)已知SKIPIF1<0,若關(guān)于x的不等式SKIPIF1<0在SKIPIF1<0上恒成立,求SKIPIF1<0的取值范圍.【C組】一、單選題1.已知A,B,C是單位圓上的三個(gè)動(dòng)點(diǎn),則AB?AC的最小值是(A.0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.設(shè)SKIPIF1<0,SKIPIF1<0,SKIPIF1<0,則a,b,c的大小順序是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0,滿足SKIPIF1<0,且當(dāng)SKIPIF1<0時(shí),SKIPIF1<0.若對(duì)任意SKIPIF1<0,都有SKIPIF1<0成立,則SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.已知冪函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增,函數(shù)SKIPIF1<0時(shí),總存在SKIPIF1<0使得SKIPIF1<0,則SKIPIF1<0的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0二、填空題5.設(shè)冪函數(shù)SKIPIF1<0的圖象過(guò)點(diǎn)SKIPIF1<0,則:①SKIPIF1<0的定義域?yàn)镾KIPIF1<0;②SKIPIF1<0是奇函數(shù);③SKIPIF1<0是減函數(shù);④當(dāng)SKIPIF1<0時(shí),SKIPIF1<0其
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