新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練8.5 奇偶性（基礎(chǔ)版）（原卷版）

8.5奇偶性（精講）（基礎(chǔ)版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一奇偶性的判斷【例1】（2022·廣東）判斷下列函數(shù)的奇偶性：（1）SKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0；（4）SKIPIF1<0.【一隅三反】1．（2022·黑龍江）下列函數(shù)中，既是偶函數(shù)又在SKIPIF1<0上不單調(diào)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·湖南衡陽·高二期末）設(shè)函數(shù)SKIPIF1<0，則下列函數(shù)中為偶函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022南京）判斷下列函數(shù)的奇偶性．(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0考點(diǎn)二利用奇偶性求解析式【例2-1】（2022·重慶巴蜀中學(xué)高三階段練習(xí)）已知SKIPIF1<0是SKIPIF1<0上的偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0時，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，那么當(dāng)SKIPIF1<0時，SKIPIF1<0的解析式是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·湖南）若函數(shù)SKIPIF1<0是定義域?yàn)镾KIPIF1<0的奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則當(dāng)SKIPIF1<0時，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南安陽）已知SKIPIF1<0是定義在R上的奇函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則當(dāng)SKIPIF1<0時，SKIPIF1<0______．考點(diǎn)三已知奇偶性求參數(shù)【例3-1】（2022·全國·高一課時練習(xí)）若函數(shù)SKIPIF1<0為奇函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．1【例3-2】．（2022·全國·長垣市）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0（

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·湖北·高三開學(xué)考試）若函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0________.2．（2022福建）若函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0軸對稱，則常數(shù)SKIPIF1<0_______.3．（2022·重慶巴蜀中學(xué)）若函數(shù)SKIPIF1<0為定義域上的奇函數(shù)，則實(shí)數(shù)SKIPIF1<0的值為______．4．（2022·云南）已知函數(shù)SKIPIF1<0是偶函數(shù)，則常數(shù)SKIPIF1<0的值為__．考點(diǎn)四利用奇偶性單調(diào)性解不等式【例4-1】（2022·全國·高一課時練習(xí)）已知偶函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，則SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例4-2】．（2022·全國·課時練習(xí)）定義在SKIPIF1<0上的偶函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，若SKIPIF1<0，則實(shí)數(shù)m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國·高三專題練習(xí)（文））設(shè)函數(shù)SKIPIF1<0，則使得SKIPIF1<0成立的SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·遼寧撫順）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·云南）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南商丘·高二期末（文））已知偶函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則使不等式SKIPIF1<0成立的實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·全國·課時練習(xí)）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，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·山西運(yùn)城）已知函數(shù)SKIPIF1<0，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)五利用奇偶性單調(diào)性比較大小【例5】（2022·北京亦莊實(shí)驗(yàn)中學(xué)）設(shè)偶函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·福建省福州第二中學(xué)）設(shè)SKIPIF1<0是定義域?yàn)镾KIPIF1<0的偶函數(shù)，且在SKIPIF1<0上單調(diào)遞減，則（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<02．（2022·陜西）已知偶函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·陜西）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且當(dāng)SKIPIF1<0時，對任意的不相等實(shí)數(shù)SKIPIF1<0總有SKIPIF1<0成立，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·內(nèi)蒙古）函數(shù)SKIPIF1<0是定義在R上的偶函數(shù)，且在SKIPIF1<0單調(diào)遞增，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08.5奇偶性（精練）（基礎(chǔ)版）題組一題組一奇偶性的判斷1．（2022·北京）下列函數(shù)中，既是偶函數(shù)又在區(qū)間SKIPIF1<0上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·專題練習(xí)）下列函數(shù)中，是偶函數(shù)且不存在零點(diǎn)的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·內(nèi)蒙古赤峰）下列函數(shù)為奇函數(shù)，且在SKIPIF1<0上為增函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·云南）（多選）下列判斷正確的是（

）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是非奇非偶函數(shù)5．（2022·廣東）（多選）已知函數(shù)SKIPIF1<0，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是奇函數(shù) B．SKIPIF1<0是奇函數(shù)C．SKIPIF1<0是偶函數(shù) D．SKIPIF1<0是偶函數(shù)6．（2022·陜西）（多選）下列函數(shù)中，既是奇函數(shù)又在區(qū)間SKIPIF1<0上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·湖南·永州市第一中學(xué)高三開學(xué)考試）（多選）下列函數(shù)中，既是偶函數(shù)又在SKIPIF1<0上單調(diào)遞增的函數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·全國·課時練習(xí)）判斷下列函數(shù)的奇偶性：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0．題組二題組二利用奇偶性求解析式1．（2022·陜西安康）已知SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則當(dāng)SKIPIF1<0時，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·云南）設(shè)SKIPIF1<0為奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，則當(dāng)SKIPIF1<0時，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·課時練習(xí)）已知SKIPIF1<0是偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，則當(dāng)SKIPIF1<0時，SKIPIF1<0_________．題組三題組三已知奇偶性求參數(shù)1．（2022·海南）若函數(shù)SKIPIF1<0是奇函數(shù)，則實(shí)數(shù)a的值為___________.2．（2022·湖北咸寧）已知函數(shù)SKIPIF1<0是奇函數(shù)，則實(shí)數(shù)SKIPIF1<0________.3．（2022·廣東深圳）若SKIPIF1<0是奇函數(shù)，則實(shí)數(shù)SKIPIF1<0___________.4．（2022·浙江·溫州中學(xué)）已知函數(shù)SKIPIF1<0是奇函數(shù)，則SKIPIF1<0___________.5．（2022·青海·海東市第一中學(xué)模擬預(yù)測（理））已知函數(shù)SKIPIF1<0，若SKIPIF1<0是奇函數(shù)，則實(shí)數(shù)a=______．6．（2022·河南安陽）已知函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0_________．7．（2022·全國·模擬預(yù)測（理））已知函數(shù)SKIPIF1<0為偶函數(shù)，則SKIPIF1<0______．8．（2022·湖北·黃岡中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0是奇函數(shù)，則實(shí)數(shù)a的值為__________．9．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0為SKIPIF1<0上的奇函數(shù)，則實(shí)數(shù)SKIPIF1<0______________________．10（2022·湖南·長郡中學(xué)模擬預(yù)測）已知函數(shù)SKIPIF1<0是奇函數(shù)，則SKIPIF1<0__________.11．（2022·貴州·貴陽市白云區(qū)第二高級中學(xué)）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0_________.12．（2022·北京·清華附中）若函數(shù)SKIPIF1<0是奇函數(shù)，則SKIPIF1<0___________，SKIPIF1<0___________.題組四題組四利用奇偶性單調(diào)性解不等式1．（2022·南京）已知偶函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，則SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·黑龍江）設(shè)SKIPIF1<0是定義在R上的奇函數(shù)，且當(dāng)SKIPIF1<0時，SKIPIF1<0，不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·四川達(dá)州）定義在R上的偶函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，則SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·上?！?fù)旦附中）設(shè)SKIPIF1<0，若SKIPIF1<0，則x的取值范圍是___________.5．（2022·福建省德化第一中學(xué)）已知函數(shù)SKIPIF1<0，使不等式SKIPIF1<0成立的一個充分不必要條件是SKIPIF1<0_________.6．（2022·全國·專題練習(xí)）已知函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為______.7．（2022·廣西玉林）已知奇函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減，且SKIPIF1<0，則不等式SKIPIF1<0的解集是___________.8．（2022·河南洛陽）已知函數(shù)SKIPIF1<0，則使得SKIPIF1<0成立的SKIPIF1<0的取值范圍是__________.題組五題組五利用奇偶性單調(diào)性比較大小1（2022·江蘇）已知函數(shù)SKIPIF1<0，則SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·北京市第十一中學(xué)）已知SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且在SKIPIF1<0上是增函數(shù)，設(shè)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．S