新高考數(shù)學(xué)一輪復(fù)習(xí)分層提升練習(xí)第09練 二次函數(shù)與冪函數(shù)（原卷版）

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_________.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_______．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?。?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_________.9．設(shè)SKIPIF1<0（SKIPIF1<0為常數(shù)），則“函數(shù)SKIPIF1<0的圖象經(jīng)過點(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．請寫出一個(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__________.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________.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__________.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