新高考数学一轮复习精讲精练3.6 零点定理（提升版）（原卷版）

3.6零点定理（精讲）（提升版）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一零点的区间【例1】（2022·河南开封·）函数SKIPIF1<0的一个零点所在的区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·湖南）函数SKIPIF1<0的零点所在区间是（

）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<02．（2022·四川攀枝花）已知函数SKIPIF1<0的零点在区间SKIPIF1<0上，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·云南德宏）方程SKIPIF1<0的解所在的区间为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点二零点的个数【例2-1】（2022·陕西）函数SKIPIF1<0的零点个数为（

）A．0 B．1 C．2 D．3【例2-2】（2022·山西）已知SKIPIF1<0若SKIPIF1<0，则SKIPIF1<0在SKIPIF1<0内的零点个数为（

）A．8 B．9 C．10 D．11【一隅三反】1．（2022·安徽）已知函数SKIPIF1<0则方程SKIPIF1<0的解的个数是（

）A．0 B．1 C．2 D．32．（2022·全国·高三专题练习）函数SKIPIF1<0的图像与函数SKIPIF1<0的图像的交点个数为（

）A．2 B．3 C．4 D．03．（2022·海南省）设函数SKIPIF1<0定义域为R，SKIPIF1<0为奇函数，SKIPIF1<0为偶函数，当SKIPIF1<0时，SKIPIF1<0，则函数SKIPIF1<0有（

）个零点A．4 B．5 C．6 D．7考点三比较零点的大小【例3】（2022·安徽）已知函数SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的零点分别为a，b，c则a，b，c的大小顺序为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·河南）若实数SKIPIF1<0满足SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·山西）正实数SKIPIF1<0满足SKIPIF1<0，则实数SKIPIF1<0之间的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点四已知零点求参数【例4-1】（2022·山东潍坊）已知函数SKIPIF1<0的图像与直线SKIPIF1<0有3个不同的交点，则实数m的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例4-2】（2022·吉林）已知SKIPIF1<0若关于x的方程SKIPIF1<0有3个不同实根，则实数SKIPIF1<0取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例4-3】（2022·安徽·合肥市）已知函数SKIPIF1<0在区间SKIPIF1<0上有且仅有4个零点，则SKIPIF1<0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）已知函数SKIPIF1<0若关于x的方程SKIPIF1<0恰有三个不相等的实数解，则m的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南·模拟预测（理））已知函数SKIPIF1<0为定义在SKIPIF1<0上的单调函数，且SKIPIF1<0．若函数SKIPIF1<0有3个零点，则SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·广西·贵港市高级中学三模）已知SKIPIF1<0在SKIPIF1<0有且仅有6个实数根，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·山西）已知函数SKIPIF1<0，若函数SKIPIF1<0恰好有两个零点，则实数k的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点五零点的综合运用【例5-1】（2022·新疆克拉玛依）函数SKIPIF1<0在区间SKIPIF1<0上的所有零点之和为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例5-2】（2022·甘肃）若函数SKIPIF1<0在区间SKIPIF1<0上有2个零点SKIPIF1<0，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例5-3】（2022·全国·高三专题练习）已知函数SKIPIF1<0的零点为SKIPIF1<0，函数SKIPIF1<0的零点为SKIPIF1<0，则下列不等式中成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·安徽·合肥一六八中学）若SKIPIF1<0为奇函数，且SKIPIF1<0是SKIPIF1<0的一个零点，则SKIPIF1<0一定是下列哪个函数的零点（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·陕西·模拟预测（理））已知SKIPIF1<0是方程SKIPIF1<0的根，SKIPIF1<0是方程SKIPIF1<0的根，则SKIPIF1<0的值为（

）A．2 B．3 C．6 D．103．（2022·陕西·西安中学一模（理））函数SKIPIF1<0的所有零点之和为_________.3.6零点定理（精练）（提升版）题组一题组一零点的区间1．（2022·甘肃·天水市第一中学）函数SKIPIF1<0的零点所在的区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02（2022·江苏扬州）函数SKIPIF1<0的零点所在的区间为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·天津红桥·一模）函数SKIPIF1<0的零点所在的区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·广东中山）函数SKIPIF1<0的零点所在的区间为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·北京师大附中）函数SKIPIF1<0的零点所在的区间是（

）A．（0，1） B．(1，2) C．(2，3) D．（3，4）6．（2022·云南玉溪·高一期末）函数SKIPIF1<0的零点所在的区间为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·宁夏·青铜峡市宁朔中学高二学业考试）函数SKIPIF1<0的零点所在的区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2022·新疆维吾尔自治区喀什第二中学）函数SKIPIF1<0的零点所在区间为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2022·海南·嘉积中学高一期末）SKIPIF1<0零点所在的区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·四川·德阳五中）函数SKIPIF1<0的零点所在的区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2022·安徽·池州市第一中学）函数SKIPIF1<0的零点所在的一个区间是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022·广东汕尾）函数SKIPIF1<0的零点所在区间为(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0题组二题组二零点的个数1．（2022·四川省泸县第二中学）函数SKIPIF1<0的零点的个数为（

）A．0 B．1 C．2 D．32．（2022·重庆）函数SKIPIF1<0的零点个数为（

）A．1 B．2 C．3 D．43．（2022·重庆·三模）已知函数SKIPIF1<0则函数SKIPIF1<0的零点个数为（

）A．0个 B．1个 C．2个 D．3个4．（2022·新疆·三模（理））函数SKIPIF1<0的零点个数为___________.5．（2022·新疆）函数SKIPIF1<0的零点个数为_________．题组三题组三比较零点的大小1．（2022·山西·二模（理））已知SKIPIF1<0是SKIPIF1<0的一个零点，SKIPIF1<0是SKIPIF1<0的一个零点，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<02．（2022·湖南·益阳市箴言中学）已知三个函数SKIPIF1<0的零点依次为SKIPIF1<0，则SKIPIF1<0的大小关系（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·陕西·长安一中模拟预测）已知函数SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的零点分别为SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，则SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的大小顺序为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·安徽·蚌埠二中模拟预测（文））已知SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·河南河南·三模）若实数SKIPIF1<0，SKIPIF1<0，SKIPIF1<0满足SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0题组四题组四已知零点求参数1．（2022·湖北宜昌）函数SKIPIF1<0，若函数SKIPIF1<0有两个零点，则实数SKIPIF1<0的取值范围是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·首都师范大学附属中学）已知函数SKIPIF1<0，若SKIPIF1<0有三个不同的零点，则实数k的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·河北唐山）已知函数SKIPIF1<0，若SKIPIF1<0有3个零点，则a的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·安徽）已知函数SKIPIF1<0在（0，+∞）上有3个不同的零点，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2022·江苏泰州·模拟预测）已知定义在R上的奇函数SKIPIF1<0满足SKIPIF1<0，已知当SKIPIF1<0时，SKIPIF1<0，若SKIPIF1<0恰有六个不相等的零点，则实数m的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·内蒙古·满洲里市教研培训中心三模（文））已知函数SKIPIF1<0有唯一零点，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·全国·高三专题练习）已知SKIPIF1<0是以2为周期的偶函数，当SKIPIF1<0时，SKIPIF1<0，那么在区间SKIPIF1<0内，关于x的方程SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）有4个根，则k的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2022·全国·高三专题练习）已知函数SKIPIF1<0与函数SKIPIF1<0的图象有两个不同的交点，则实数m取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2022·天津·南开中学模拟预测）已知函数SKIPIF1<0，若函数SKIPIF1<0恰有两个零点则实数SKIPIF1<0的取值范围是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2022·天津南开·二模）已知定义在SKIPIF1<0上的函数SKIPIF1<0若函数SKIPIF1<0恰有2个零点，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<011．（2022·陕西·模拟预测（理））已知函数SKIPIF1<0SKIPIF1<0在SKIPIF1<0上有且只有5个零点，则实数SKIPIF1<0的范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022·陕西宝鸡·二模（文））已知函数SKIPIF1<0（SKIPIF1<0是自然对数的底数）在定义域SKIPIF1<0上有三个零点，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2022·全国·高三专题练习）已知函数SKIPIF1<0在区间SKIPIF1<0上既有极大值又有极小值，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2022·河南·模拟预测（理））已知函数SKIPIF1<0至多有2个不同的零点，则实数a的最大值为（

）．A．0 B．1 C．2 D．e15（2022·天津市武清区杨村第一中学二模）设SKIPIF1<0，函数SKIPIF1<0．若SKIPIF1<0在SKIPIF1<0上单调递增，且函数SKIPIF1<0与SKIPIF1<0的图象有三个交点，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．