新高考數(shù)學(xué)一輪復(fù)習(xí) 函數(shù)專項(xiàng)重難點(diǎn)突破專題12 函數(shù)的基本性質(zhì)綜合測(cè)試(原卷版)

專題12函數(shù)的基本性質(zhì)綜合測(cè)試考試時(shí)間：120分鐘滿分：150分一、單選題：本大題共8小題，每個(gè)小題5分，共40分.在每小題給出的選項(xiàng)中，只有一項(xiàng)是符合題目要求的.1．已知SKIPIF1<0是偶函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．22．設(shè)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0的定義域均為R，且SKIPIF1<0．若SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對(duì)稱，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知定義在SKIPIF1<0的函數(shù)滿足SKIPIF1<0，SKIPIF1<0，則下列結(jié)論正確的是（

）A．SKIPIF1<0不是周期函數(shù)B．SKIPIF1<0是奇函數(shù)C．對(duì)任意SKIPIF1<0，恒有SKIPIF1<0為定值D．對(duì)任意SKIPIF1<0，有SKIPIF1<05．已知函數(shù)SKIPIF1<0滿足當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0且SKIPIF1<0).若函數(shù)SKIPIF1<0的圖象上關(guān)于原點(diǎn)對(duì)稱的點(diǎn)恰好有3對(duì)，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0是奇函數(shù)，且滿足SKIPIF1<0，SKIPIF1<0，數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的前SKIPIF1<0項(xiàng)和，SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．47．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0．其圖象關(guān)于原點(diǎn)成中心對(duì)稱，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0為偶函數(shù)，SKIPIF1<0為奇函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題：本大題共4小題，每個(gè)小題5分，共20分.在每小題給出的選項(xiàng)中，只有一項(xiàng)或者多項(xiàng)是符合題目要求的.9．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0，則（

）．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0是偶函數(shù) D．SKIPIF1<0為SKIPIF1<0的極小值點(diǎn)10．已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均為SKIPIF1<0，記SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0均為偶函數(shù)，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0為奇函數(shù)，則（

）A．函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對(duì)稱B．函數(shù)SKIPIF1<0是周期函數(shù)C．SKIPIF1<0D．SKIPIF1<012．已知函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0的定義域均為SKIPIF1<0.SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0的圖象關(guān)于SKIPIF1<0對(duì)稱 B．SKIPIF1<0為偶函數(shù)C．SKIPIF1<0 D．不等式SKIPIF1<0的解集為SKIPIF1<0三、填空題：本大題共4小題，每小題5分，共20分.把答案填在答題卡中的橫線上.13．若SKIPIF1<0為偶函數(shù)，則SKIPIF1<0________．14．已知函數(shù)SKIPIF1<0，則使得SKIPIF1<0成立的實(shí)數(shù)SKIPIF1<0的取值范圍為_(kāi)_________.15．設(shè)SKIPIF1<0為定義在SKIPIF1<0上的可導(dǎo)函數(shù)，其導(dǎo)函數(shù)SKIPIF1<0為偶函數(shù)，若對(duì)任意SKIPIF1<0有SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0__________.16．若SKIPIF1<0是奇函數(shù)，則SKIPIF1<0_____，SKIPIF1<0______．四、解答題：本大題共6小題，共70分.解答應(yīng)寫出必要的文字說(shuō)明、證明過(guò)程或演算步驟．17．設(shè)函數(shù)SKIPIF1<0滿足SKIPIF1<0.(1)判定SKIPIF1<0的奇偶性并說(shuō)明理由；(2)當(dāng)SKIPIF1<0為奇函數(shù)時(shí)，是否存在常數(shù)SKIPIF1<0，使得關(guān)于SKIPIF1<0的不等式SKIPIF1<0在區(qū)間SKIPIF1<0上的解集非空，若存在，求出SKIPIF1<0的取值范圍；若不存在，請(qǐng)說(shuō)明理由.18．已知函數(shù)SKIPIF1<0對(duì)于任意SKIPIF1<0，總有SKIPIF1<0，且SKIPIF1<0時(shí)，SKIPIF1<0.(1)求證：SKIPIF1<0在SKIPIF1<0上是奇函數(shù)；(2)求證：SKIPIF1<0在SKIPIF1<0上是減函數(shù)；(3)若SKIPIF1<0，求SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值和最小值.19．已知函數(shù)SKIPIF1<0，該函數(shù)我們可以看作是函數(shù)SKIPIF1<0與SKIPIF1<0相加，利用這兩個(gè)函數(shù)的性質(zhì)，我們可以探究SKIPIF1<0的函數(shù)性質(zhì)．

(1)求出SKIPIF1<0的最小正周期；(2)寫出SKIPIF1<0的所有對(duì)稱中心（不需要說(shuō)明理由）；(3)求使SKIPIF1<0成立的x的取值的集合．20．已知函數(shù)f（x）＝SKIPIF1<0是定義在R上的奇函數(shù)．(1)求實(shí)數(shù)a的值；(2)證明：函數(shù)f（x）在R上單調(diào)遞增；(3)記SKIPIF1<0，對(duì)SKIPIF1<0x∈R，不等式SKIPIF1<0恒成立，求實(shí)數(shù)m的取值范圍．21．設(shè)函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的函數(shù)，若存在SKIPIF1<0，使得SKIPIF1<0在SKIPIF1<0上是嚴(yán)格增函數(shù)，在SKIPIF1<0上是嚴(yán)格減函數(shù)，則稱SKIPIF1<0為SKIPIF1<0上的單峰函數(shù)，SKIPIF1<0稱為峰點(diǎn)，SKIPIF1<0稱為含峰區(qū)間，(1)判斷下列函數(shù)中，哪些是“SKIPIF1<0上的單峰函數(shù)”？若是，指出峰點(diǎn)；若不是，說(shuō)出原因：SKIPIF1<0，SKIPIF1<0；(2)若函數(shù)SKIPIF1<0是區(qū)間SKIPIF1<0上的單峰函數(shù)，求實(shí)數(shù)SKIPIF1<0的取值范圍.22．已知函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0成中心對(duì)稱圖形的充要條件是SKIPIF1<0．給定函數(shù)SKIPIF1<0及其圖象的對(duì)稱中心為SKIPI