新高考數(shù)學(xué)一輪復(fù)習(xí) 專項(xiàng)分層精練第06課 奇偶性、對稱性與周期性（原卷版）

第03課奇偶性、對稱性與周期性（分層專項(xiàng)精練）【一層練基礎(chǔ)】一、單選題1．（2022秋·甘肅武威·高三武威第六中學(xué)?？茧A段練習(xí)）下列函數(shù)中，既是偶函數(shù)又在SKIPIF1<0上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2021·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0為奇函數(shù)，則實(shí)數(shù)SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022秋·高一單元測試）函數(shù)SKIPIF1<0在SKIPIF1<0單調(diào)遞減，且為奇函數(shù)．若SKIPIF1<0，則滿足SKIPIF1<0的SKIPIF1<0的取值范圍是（

）A．[－2，2] B．[－1，2] C．[0，4] D．[1，3]4．（2022秋·廣東肇慶·高一德慶縣香山中學(xué)校考期中）設(shè)函數(shù)SKIPIF1<0是定義在實(shí)數(shù)集上的奇函數(shù)，在區(qū)間SKIPIF1<0上是增函數(shù)，且SKIPIF1<0，則有A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022秋·福建泉州·高一石獅市第一中學(xué)?？计谥校┮阎猄KIPIF1<0是定義在SKIPIF1<0，SKIPIF1<0上的偶函數(shù)，且在SKIPIF1<0，SKIPIF1<0上為增函數(shù)，則SKIPIF1<0的解集為SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022秋·高一課時練習(xí)）已知偶函數(shù)f(x)在區(qū)間SKIPIF1<0單調(diào)遞增，則滿足SKIPIF1<0的x取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023春·江蘇蘇州·高二常熟中學(xué)?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0為偶函數(shù)，且函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則關(guān)于x的不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題8．（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且SKIPIF1<0與SKIPIF1<0都為奇函數(shù)，則下列說法正確的是（

）A．SKIPIF1<0是周期為SKIPIF1<0的周期函數(shù) B．SKIPIF1<0是周期為SKIPIF1<0的周期函數(shù)C．SKIPIF1<0為奇函數(shù) D．SKIPIF1<0為奇函數(shù)9．（2022春·江蘇鹽城·高一江蘇省響水中學(xué)?？奸_學(xué)考試）SKIPIF1<0是定義在SKIPIF1<0上周期為4的函數(shù)，且SKIPIF1<0，則下列說法中正確的是（

）A．SKIPIF1<0SKIPIF1<0的值域?yàn)镾KIPIF1<0B．當(dāng)SKIPIF1<0時，SKIPIF1<0C．SKIPIF1<0圖象的對稱軸為直線SKIPIF1<0D．方程SKIPIF1<0恰有5個實(shí)數(shù)解10．（2023春·高一單元測試）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足條件SKIPIF1<0，且函數(shù)SKIPIF1<0為奇函數(shù)，則（

）A．函數(shù)SKIPIF1<0是周期函數(shù) B．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對稱C．函數(shù)SKIPIF1<0為SKIPIF1<0上的偶函數(shù) D．函數(shù)SKIPIF1<0為SKIPIF1<0上的單調(diào)函數(shù)11．（2023春·安徽滁州·高一?？茧A段練習(xí)）已知SKIPIF1<0是定義在R上的偶函數(shù)，且對任意SKIPIF1<0，有SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則（

）A．SKIPIF1<0是以2為周期的周期函數(shù)B．點(diǎn)SKIPIF1<0是函數(shù)SKIPIF1<0的一個對稱中心C．SKIPIF1<0D．函數(shù)SKIPIF1<0有3個零點(diǎn)12．（2020·全國·高三專題練習(xí)）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，下列等式成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0對SKIPIF1<0，都有SKIPIF1<0，SKIPIF1<0為奇函數(shù)，且SKIPIF1<0時，SKIPIF1<0，下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0中心對稱B．SKIPIF1<0是周期為2的函數(shù)C．SKIPIF1<0D．SKIPIF1<0三、填空題14．（2023·全國·高三專題練習(xí)）我們知道，函數(shù)SKIPIF1<0的圖象關(guān)于坐標(biāo)原點(diǎn)成中心對稱圖形的充要條件是函數(shù)SKIPIF1<0為奇函數(shù)，有同學(xué)發(fā)現(xiàn)可以將其推廣為：函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0成中心對稱圖形的充要條件是函數(shù)SKIPIF1<0為奇函數(shù)，則SKIPIF1<0的圖象的對稱中心為.15．（2022秋·江西宜春·高三江西省豐城中學(xué)校考開學(xué)考試）寫出一個同時具有下列性質(zhì)①②③的函數(shù)SKIPIF1<0.①SKIPIF1<0是定義域?yàn)镾KIPIF1<0的奇函數(shù)；②SKIPIF1<0；③SKIPIF1<0.16．（2020·全國·高三專題練習(xí)）已知SKIPIF1<0，函數(shù)SKIPIF1<0為偶函數(shù)，且在SKIPIF1<0上是減函數(shù)，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為．17．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則SKIPIF1<0．18．（2020秋·內(nèi)蒙古包頭·高一包頭市第六中學(xué)?？计谥校┮阎瘮?shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對稱，則SKIPIF1<0．【二層練綜合】一、單選題1．（2023·全國·高三專題練習(xí)）已知定義在R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0是奇函數(shù)，則（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱C．SKIPIF1<0是奇函數(shù) D．SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對稱2．（2022·江西贛州·贛州市贛縣第三中學(xué)?？寄M預(yù)測）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．對任意SKIPIF1<0，恒有SKIPIF1<0為定值D．對任意SKIPIF1<0，有SKIPIF1<03．（2022秋·四川遂寧·高三?？茧A段練習(xí)）若函數(shù)SKIPIF1<0為偶函數(shù)，對任意的SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022秋·陜西安康·高三?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，對任意的SKIPIF1<0都有SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·四川廣安·四川省廣安友誼中學(xué)?？寄M預(yù)測）已知定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則下列不等式正確的是A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的定義域?yàn)镽，SKIPIF1<0，且SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題7．（2023·廣東梅州·大埔縣虎山中學(xué)?？寄M預(yù)測）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0．則下列結(jié)論正確的是（

）．A．當(dāng)SKIPIF1<0時，SKIPIF1<0B．函數(shù)SKIPIF1<0有五個零點(diǎn)C．若關(guān)于SKIPIF1<0的方程SKIPIF1<0有解，則實(shí)數(shù)SKIPIF1<0的取值范圍是SKIPIF1<0D．對SKIPIF1<0，SKIPIF1<0恒成立8．（2023·全國·高三專題練習(xí)）關(guān)于函數(shù)SKIPIF1<0有以下四個選項(xiàng)，正確的是（

）A．對任意的a，SKIPIF1<0都不是偶函數(shù) B．存在a，使SKIPIF1<0是奇函數(shù)C．存在a，使SKIPIF1<0 D．若SKIPIF1<0的圖像關(guān)于SKIPIF1<0對稱，則SKIPIF1<09．（2023春·甘肅張掖·高一高臺縣第一中學(xué)校考階段練習(xí)）已知函數(shù)SKIPIF1<0是定義在R上的奇函數(shù)，SKIPIF1<0是偶函數(shù)，當(dāng)SKIPIF1<0，則下列說法中正確的有（

）A．函數(shù)SKIPIF1<0關(guān)于直線SKIPIF1<0對稱B．4是函數(shù)SKIPIF1<0的周期C．SKIPIF1<0D．方程SKIPIF1<0恰有4不同的根10．（2023春·安徽·高二馬鞍山二中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0）是奇函數(shù)，SKIPIF1<0且SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的導(dǎo)函數(shù)，則（

）A．SKIPIF1<0 B．SKIPIF1<0的一個周期是4 C．SKIPIF1<0是偶函數(shù)D．SKIPIF1<011．（2022春·湖南長沙·高二長郡中學(xué)?？计谀┮阎x在R上的函數(shù)f(x)滿足f(x)=f(-x)，f(x+1)=f(1-x)，且當(dāng)x∈[0，1]時，f(x)=-x2+2x，則下列結(jié)論正確的是（

）A．f(x)的圖象關(guān)于直線x=1對稱 B．當(dāng)SKIPIF1<0時，SKIPIF1<0C．當(dāng)SKIPIF1<0時，f(x)單調(diào)遞增 D．SKIPIF1<012．（2023春·山東臨沂·高二?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0為SKIPIF1<0上的奇函數(shù)，SKIPIF1<0為偶函數(shù)，下列說法正確的有（

）A．SKIPIF1<0圖象關(guān)于直線SKIPIF1<0對稱 B．SKIPIF1<0C．SKIPIF1<0的最小正周期為4 D．對任意SKIPIF1<0都有SKIPIF1<0三、填空題13．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0為R上的奇函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0的值為．14．（2022秋·山東菏澤·高一校考階段練習(xí)）設(shè)奇函數(shù)f(x)在(0，＋∞)上為增函數(shù)，且f(1)＝0，則不等式SKIPIF1<0<0的解集為.15．（2021秋·上海靜安·高三上海市第六十中學(xué)?？茧A段練習(xí)）設(shè)SKIPIF1<0是定義在R上以2為周期的偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則函數(shù)SKIPIF1<0在SKIPIF1<0上的解析式是16．（2022春·江西吉安·高二校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，若對于SKIPIF1<0，都有SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0的值為.17．（2022·高二課時練習(xí)）已知函數(shù)SKIPIF1<0的圖象是以點(diǎn)SKIPIF1<0為中心的中心對稱圖形，SKIPIF1<0，曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線互相垂直，則SKIPIF1<0．18．（2023·貴州銅仁·統(tǒng)考模擬預(yù)測）關(guān)于函數(shù)SKIPIF1<0，有如下四個命題：①若SKIPIF1<0，則SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0對稱；②若SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，則SKIPIF1<0；③當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0的極值為SKIPIF1<0；④當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0有兩個零點(diǎn)．其中所有真命題的序號是．【三層練能力】一、單選題1．（2023·黑龍江哈爾濱·哈師大附中?？寄M預(yù)測）函數(shù)SKIPIF1<0、SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023·江西·統(tǒng)考模擬預(yù)測）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，若SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，記SKIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·河南·校聯(lián)考模擬預(yù)測）已知SKIPIF1<0是定義在SKIPIF1<0上的函數(shù)，且SKIPIF1<0為奇函數(shù)，SKIPIF1<0為偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題4．（2023春·陜西渭南·高一統(tǒng)考期末）已知函數(shù)SKIPIF1<0、