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07 函數(shù)的奇偶性(原卷版)

專題07函數(shù)的奇偶性真題再現(xiàn)一、單選題1．（2023·全國(guó)·統(tǒng)考高考真題）若SKIPIF1<0為偶函數(shù)，則SKIPIF1<0（

）．A．SKIPIF1<0 B．0 C．SKIPIF1<0 D．12．（2023·全國(guó)·統(tǒng)考高考真題）已知SKIPIF1<0是偶函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．23．（2023·天津·統(tǒng)考高考真題）函數(shù)SKIPIF1<0的圖象如下圖所示，則SKIPIF1<0的解析式可能為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·天津·統(tǒng)考高考真題）函數(shù)SKIPIF1<0的圖像為（

）A． B．C． D．5．（2022·全國(guó)·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0的定義域?yàn)镽，且SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．16．（2021·全國(guó)·統(tǒng)考高考真題）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)，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2021·全國(guó)·高考真題）設(shè)SKIPIF1<0是定義域?yàn)镽的奇函數(shù)，且SKIPIF1<0.若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2021·全國(guó)·統(tǒng)考高考真題）設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镽，SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2021·全國(guó)·統(tǒng)考高考真題）設(shè)函數(shù)SKIPIF1<0，則下列函數(shù)中為奇函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題10．（2023·全國(guó)·統(tǒng)考高考真題）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)11．（2022·全國(guó)·統(tǒng)考高考真題）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<0三、填空題12．（2023·全國(guó)·統(tǒng)考高考真題）若SKIPIF1<0為偶函數(shù)，則SKIPIF1<0________．13．（2021·全國(guó)·統(tǒng)考高考真題）寫出一個(gè)同時(shí)具有下列性質(zhì)①②③的函數(shù)SKIPIF1<0_______．①SKIPIF1<0；②當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0；③SKIPIF1<0是奇函數(shù)．14．（2021·全國(guó)·統(tǒng)考高考真題）已知函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0______.四、雙空題15．（2022·全國(guó)·統(tǒng)考高考真題）若SKIPIF1<0是奇函數(shù)，則SKIPIF1<0_____，SKIPIF1<0______．考點(diǎn)一奇偶性的判斷或證明一、多選題1．以下函數(shù)的圖象是中心對(duì)稱圖形的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．設(shè)函數(shù)SKIPIF1<0的定義域都為R，且SKIPIF1<0是奇函數(shù)，SKIPIF1<0是偶函數(shù)，則下列結(jié)論正確的是（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0是奇函數(shù)C．SKIPIF1<0是奇函數(shù) D．SKIPIF1<0是偶函數(shù)3．若函數(shù)SKIPIF1<0在其定義域內(nèi)是奇函數(shù)或偶函數(shù)，則稱SKIPIF1<0具有奇偶性.以下函數(shù)中，具有奇偶性的函數(shù)是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0二、單選題4．設(shè)函數(shù)SKIPIF1<0，則下列函數(shù)中為奇函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．函數(shù)SKIPIF1<0（

）A．是奇函數(shù) B．是偶函數(shù)C．既是奇函數(shù)又是偶函數(shù) D．既不是奇函數(shù)也不是偶函數(shù)6．定義在R上的函數(shù)SKIPIF1<0滿足：①SKIPIF1<0，②SKIPIF1<0是奇函數(shù)，則下列結(jié)論可能不正確的是（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0關(guān)于x＝1對(duì)稱7．若定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足：對(duì)于任意的SKIPIF1<0、SKIPIF1<0，恒有SKIPIF1<0，則函數(shù)SKIPIF1<0為（

）A．奇函數(shù) B．偶函數(shù) C．非奇非偶函數(shù) D．無法判斷奇偶性三、解答題8．已知函數(shù)SKIPIF1<0（SKIPIF1<0，且SKIPIF1<0）.(1)證明：函數(shù)SKIPIF1<0是偶函數(shù)；(2)若SKIPIF1<0在定義域上恒成立，求SKIPIF1<0的取值范圍.9．判斷下列函數(shù)的奇偶性：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<010．判斷下列函數(shù)的奇偶性：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0．11．若定義在R上的函數(shù)SKIPIF1<0滿足：SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0成立，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.(1)求證：SKIPIF1<0為奇函數(shù)；(2)求證：SKIPIF1<0為SKIPIF1<0上的增函數(shù)12．設(shè)定義在SKIPIF1<0上的函數(shù)SKIPIF1<0對(duì)任意SKIPIF1<0均滿足：SKIPIF1<0，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0.(1)判斷并證明SKIPIF1<0的奇偶性；(2)判斷并證明SKIPIF1<0在SKIPIF1<0上的單調(diào)性；(3)若SKIPIF1<0，解不等式SKIPIF1<0.考點(diǎn)二利用奇偶性求函數(shù)值或解析式一、單選題1．已知函數(shù)SKIPIF1<0是定義域?yàn)镾KIPIF1<0的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．1 B．－1 C．5 D．－52．已知SKIPIF1<0（其中SKIPIF1<0為常數(shù)且SKIPIF1<0），如果SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．53．已知SKIPIF1<0，則SKIPIF1<0等于（

）A．8 B．SKIPIF1<0 C．SKIPIF1<0 D．104．SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，且SKIPIF1<0則SKIPIF1<0（

）A．3 B．-1 C．1 D．-35．已知函數(shù)SKIPIF1<0在SKIPIF1<0上的最大值與最小值分別為SKIPIF1<0和SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．0 C．2 D．46．已知函數(shù)SKIPIF1<0在SKIPIF1<0上為偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的解析式是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0是偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，那么當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的解析式是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0為定義在R上的奇函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則SKIPIF1<0（

）A．﹣2022 B．2022 C．SKIPIF1<0 D．SKIPIF1<0二、填空題9．已知SKIPIF1<0為奇函數(shù)，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0__________.10．設(shè)SKIPIF1<0為實(shí)數(shù)，函數(shù)SKIPIF1<0是奇函數(shù)，則SKIPIF1<0__．11．若函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，則SKIPIF1<0______．12．已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0則SKIPIF1<0__．考點(diǎn)三由奇偶性解不等式一、單選題1．函數(shù)SKIPIF1<0是R上的偶函數(shù)，且在SKIPIF1<0上是增函數(shù)，若SKIPIF1<0，則a的取值范圍是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<0或SKIPIF1<02．已知SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知偶函數(shù)SKIPIF1<0，則滿足SKIPIF1<0的實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且在SKIPIF1<0上單調(diào)遞減，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，則滿足SKIPIF1<0的SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0是定義在R上的偶函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且在SKIPIF1<0上單調(diào)遞增，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題8．已知函數(shù)SKIPIF1<0在R上單調(diào)遞減，且為奇函數(shù)，若SKIPIF1<0，則滿足SKIPIF1<0的x值可能為（

）A．SKIPIF1<0 B．0 C．1 D．2三、填空題9．定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0滿足：在SKIPIF1<0上單調(diào)遞減，則滿足SKIPIF1<0的解集________.10．定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，若SKIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為_____.11．設(shè)奇函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，若當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的圖象如下圖，則不等式SKIPIF1<0的解是______．12．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的取值范圍是__________.四、雙空題13．SKIPIF1<0是定義在SKIPIF1<0上單調(diào)遞增的奇函數(shù)，則SKIPIF1<0________；若SKIPIF1<0，則x的取值范圍為________.五、解答題14．已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)用定義法證明：函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增；(2)求不等式SKIPIF1<0的解集．15．已知定義在SKIPIF1<0的函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞減，且SKIPIF1<0.(1)若SKIPIF1<0是奇函數(shù)，求m的取值范圍；(2)若SKIPIF1<0是偶函數(shù)，求m的取值范圍.16．已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)．(1)求實(shí)數(shù)SKIPIF1<0的值；(2)若不等式SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．17．已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的解析式．(2)若SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的取值范圍．18．函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且SKIPIF1<0．(1)確定SKIPIF1<0的解析式；(2)判斷SKIPIF1<0在SKIPIF1<0上的單調(diào)性，并證明你的結(jié)論；(3)解關(guān)于SKIPIF1<0的不等式SKIPIF1<0．考點(diǎn)四利用奇偶性求參一、單選題1．已知SKIPIF1<0是偶函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0B．1 C．SKIPIF1<0 D．22．已知函數(shù)SKIPIF1<0是奇函數(shù)，則SKIPIF1<0（

）A．0 B．1 C．SKIPIF1<0 D．SKIPIF1<03．若函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0