新高考数学一轮复习精讲精练8.5 奇偶性（基础版）（原卷版）

8.5奇偶性（精讲）（基础版）思维导图思维导图考点呈现考点呈现例题剖析例题剖析考点一奇偶性的判断【例1】（2022·广东）判断下列函数的奇偶性：（1）SKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0；（4）SKIPIF1<0.【一隅三反】1．（2022·黑龙江）下列函数中，既是偶函数又在SKIPIF1<0上不单调的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·湖南衡阳·高二期末）设函数SKIPIF1<0，则下列函数中为偶函数的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022南京）判断下列函数的奇偶性．(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0考点二利用奇偶性求解析式【例2-1】（2022·重庆巴蜀中学高三阶段练习）已知SKIPIF1<0是SKIPIF1<0上的偶函数，当SKIPIF1<0时，SKIPIF1<0，则SKIPIF1<0时，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·全国·高三专题练习）已知函数SKIPIF1<0是奇函数，且当SKIPIF1<0时，SKIPIF1<0，那么当SKIPIF1<0时，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）若函数SKIPIF1<0是定义域为SKIPIF1<0的奇函数，且当SKIPIF1<0时，SKIPIF1<0，则当SKIPIF1<0时，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南安阳）已知SKIPIF1<0是定义在R上的奇函数，当SKIPIF1<0时，SKIPIF1<0，则当SKIPIF1<0时，SKIPIF1<0______．考点三已知奇偶性求参数【例3-1】（2022·全国·高一课时练习）若函数SKIPIF1<0为奇函数，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．1【例3-2】．（2022·全国·长垣市）已知函数SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0（

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·湖北·高三开学考试）若函数SKIPIF1<0是偶函数，则SKIPIF1<0________.2．（2022福建）若函数SKIPIF1<0的图象关于SKIPIF1<0轴对称，则常数SKIPIF1<0_______.3．（2022·重庆巴蜀中学）若函数SKIPIF1<0为定义域上的奇函数，则实数SKIPIF1<0的值为______．4．（2022·云南）已知函数SKIPIF1<0是偶函数，则常数SKIPIF1<0的值为__．考点四利用奇偶性单调性解不等式【例4-1】（2022·全国·高一课时练习）已知偶函数SKIPIF1<0的定义域为SKIPIF1<0，当SKIPIF1<0时，SKIPIF1<0，则SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例4-2】．（2022·全国·课时练习）定义在SKIPIF1<0上的偶函数SKIPIF1<0在区间SKIPIF1<0上单调递减，若SKIPIF1<0，则实数m的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全国·高三专题练习（文））设函数SKIPIF1<0，则使得SKIPIF1<0成立的SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·辽宁抚顺）定义在SKIPIF1<0上的奇函数SKIPIF1<0在SKIPIF1<0上单调递增，则不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·云南）已知函数SKIPIF1<0是定义在SKIPIF1<0上的偶函数，当SKIPIF1<0时，SKIPIF1<0，则不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·河南商丘·高二期末（文））已知偶函数SKIPIF1<0的定义域为SKIPIF1<0，且当SKIPIF1<0时，SKIPIF1<0，则使不等式SKIPIF1<0成立的实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·全国·课时练习）定义在SKIPIF1<0上的奇函数SKIPIF1<0在SKIPIF1<0上单调递增，且SKIPIF1<0，则不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·山西运城）已知函数SKIPIF1<0，则关于SKIPIF1<0的不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点五利用奇偶性单调性比较大小【例5】（2022·北京亦庄实验中学）设偶函数SKIPIF1<0在区间SKIPIF1<0上单调递增，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·福建省福州第二中学）设SKIPIF1<0是定义域为SKIPIF1<0的偶函数，且在SKIPIF1<0上单调递减，则（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<02．（2022·陕西）已知偶函数SKIPIF1<0在SKIPIF1<0上单调递减，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·陕西）已知函数SKIPIF1<0是定义在SKIPIF1<0上的偶函数，且当SKIPIF1<0时，对任意的不相等实数SKIPIF1<0总有SKIPIF1<0成立，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·内蒙古）函数SKIPIF1<0是定义在R上的偶函数，且在SKIPIF1<0单调递增，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08.5奇偶性（精练）（基础版）题组一题组一奇偶性的判断1．（2022·北京）下列函数中，既是偶函数又在区间SKIPIF1<0上单调递增的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全国·专题练习）下列函数中，是偶函数且不存在零点的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·内蒙古赤峰）下列函数为奇函数，且在SKIPIF1<0上为增函数的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·云南）（多选）下列判断正确的是（

）A．SKIPIF1<0是偶函数 B．SKIPIF1<0是奇函数C．SKIPIF1<0是奇函数 D．SKIPIF1<0是非奇非偶函数5．（2022·广东）（多选）已知函数SKIPIF1<0，SKIPIF1<0的定义域都为R，且SKIPIF1<0是奇函数，SKIPIF1<0是偶函数，则下列结论正确的是（

）A．SKIPIF1<0是奇函数 B．SKIPIF1<0是奇函数C．SKIPIF1<0是偶函数 D．SKIPIF1<0是偶函数6．（2022·陕西）（多选）下列函数中，既是奇函数又在区间SKIPIF1<0上单调递增的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·湖南·永州市第一中学高三开学考试）（多选）下列函数中，既是偶函数又在SKIPIF1<0上单调递增的函数是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·全国·课时练习）判断下列函数的奇偶性：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0；(4)SKIPIF1<0．题组二题组二利用奇偶性求解析式1．（2022·陕西安康）已知SKIPIF1<0是定义在SKIPIF1<0上的奇函数，且当SKIPIF1<0时，SKIPIF1<0，则当SKIPIF1<0时，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·云南）设SKIPIF1<0为奇函数，且当SKIPIF1<0时，SKIPIF1<0，则当SKIPIF1<0时，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全国·课时练习）已知SKIPIF1<0是偶函数，当SKIPIF1<0时，SKIPIF1<0，则当SKIPIF1<0时，SKIPIF1<0_________．题组三题组三已知奇偶性求参数1．（2022·海南）若函数SKIPIF1<0是奇函数，则实数a的值为___________.2．（2022·湖北咸宁）已知函数SKIPIF1<0是奇函数，则实数SKIPIF1<0________.3．（2022·广东深圳）若SKIPIF1<0是奇函数，则实数SKIPIF1<0___________.4．（2022·浙江·温州中学）已知函数SKIPIF1<0是奇函数，则SKIPIF1<0___________.5．（2022·青海·海东市第一中学模拟预测（理））已知函数SKIPIF1<0，若SKIPIF1<0是奇函数，则实数a=______．6．（2022·河南安阳）已知函数SKIPIF1<0是偶函数，则SKIPIF1<0_________．7．（2022·全国·模拟预测（理））已知函数SKIPIF1<0为偶函数，则SKIPIF1<0______．8．（2022·湖北·黄冈中学模拟预测）已知函数SKIPIF1<0是奇函数，则实数a的值为__________．9．（2022·全国·高三专题练习）已知函数SKIPIF1<0为SKIPIF1<0上的奇函数，则实数SKIPIF1<0______________________．10（2022·湖南·长郡中学模拟预测）已知函数SKIPIF1<0是奇函数，则SKIPIF1<0__________.11．（2022·贵州·贵阳市白云区第二高级中学）已知函数SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0_________.12．（2022·北京·清华附中）若函数SKIPIF1<0是奇函数，则SKIPIF1<0___________，SKIPIF1<0___________.题组四题组四利用奇偶性单调性解不等式1．（2022·南京）已知偶函数SKIPIF1<0在SKIPIF1<0上单调递增，且SKIPIF1<0，则SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·黑龙江）设SKIPIF1<0是定义在R上的奇函数，且当SKIPIF1<0时，SKIPIF1<0，不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·四川达州）定义在R上的偶函数SKIPIF1<0在SKIPIF1<0上单调递增，且SKIPIF1<0，则SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·上海·复旦附中）设SKIPIF1<0，若SKIPIF1<0，则x的取值范围是___________.5．（2022·福建省德化第一中学）已知函数SKIPIF1<0，使不等式SKIPIF1<0成立的一个充分不必要条件是SKIPIF1<0_________.6．（2022·全国·专题练习）已知函数SKIPIF1<0，则不等式SKIPIF1<0的解集为______.7．（2022·广西玉林）已知奇函数SKIPIF1<0在区间SKIPIF1<0上单调递减，且SKIPIF1<0，则不等式SKIPIF1<0的解集是___________.8．（2022·河南洛阳）已知函数SKIPIF1<0，则使得SKIPIF1<0成立的SKIPIF1<0的取值范围是__________.题组五题组五利用奇偶性单调性比较大小1（2022·江苏）已知函数SKIPIF1<0，则SKIPIF1<0的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·北京市第十一中学）已知SKIPIF1<0是定义在SKIPIF1<0上的偶函数，且在SKIPIF1<0上是增函数，设SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的大小关系是（

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