新高考数学一轮复习提升训练3.3 指数运算及指数函数（精讲）（原卷版）

3.3指数运算及指数函数（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指数运算【例1-1】（2022·江西）化简SKIPIF1<0___.【例1-2】（2022·江苏）化简：SKIPIF1<0________．【一隅三反】1．（2022·河南）SKIPIF1<0_____．2．（2022·全国·高三专题练习）SKIPIF1<0×SKIPIF1<00＋80.25×SKIPIF1<0＋(SKIPIF1<0×SKIPIF1<0)6－SKIPIF1<0=____________3．（2021·江苏省）已知SKIPIF1<0，则SKIPIF1<0的值为___________．考点二单调性【例2-1】（2021·安徽）函数SKIPIF1<0的单调递增区间为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2021·北京市）已知函数SKIPIF1<0|在区间SKIPIF1<0上是增函数，则实数SKIPIF1<0的取值范围是_____.【例2-3】（2022·河南省）已知函数SKIPIF1<0满足对任意的实数SKIPIF1<0，且SKIPIF1<0，都有SKIPIF1<0成立，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·辽宁沈阳）已知函数SKIPIF1<0，则函数SKIPIF1<0（

）A．是偶函数，且在SKIPIF1<0上单调递增B．是奇函数，且在SKIPIF1<0上单调递减C．是奇函数，且在SKIPIF1<0上单调递增D．是偶函数，且在SKIPIF1<0上单调递减2．（2022·全国·高三专题练习）已知函数SKIPIF1<0满足对任意x1≠x2，都有(x1-x2)[f(x1)-f(x2)]<0成立，则a的取值范围为（）A．SKIPIF1<0 B．(0，1) C．SKIPIF1<0 D．(0，3)3．（2022·上海奉贤区致远高级中学高三开学考试）函数SKIPIF1<0在SKIPIF1<0内单调递增，则实数SKIPIF1<0的取值范围是__________.考点三最值（值域）【例3-1】（2022·北京·高三专题练习）已知函数SKIPIF1<0，SKIPIF1<0，则函数SKIPIF1<0的值域为（

）．A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-2】（2022·北京）已知函数SKIPIF1<0的值域为R，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·宁夏）已知SKIPIF1<0的最小值为2，则SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·浙江·高三专题练习）已知函数SKIPIF1<0，则函数SKIPIF1<0在区间SKIPIF1<0上的最小值的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·河南）若函数SKIPIF1<0的值域为SKIPIF1<0，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全国·高三专题练习）已知SKIPIF1<0，则函数SKIPIF1<0的值域为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022·河南焦作·二模（理））已知函数SKIPIF1<0为奇函数，且SKIPIF1<0的图象和函数SKIPIF1<0的图象交于不同的两点A，B，若线段SKIPIF1<0的中点SKIPIF1<0在直线SKIPIF1<0上，则SKIPIF1<0的值域为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考点四指数式比较大小【例4-1】（2022·河南焦作）若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，a，b，c的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例4-2】（2022·江西·二模（理））设SKIPIF1<0，则(

)A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·河南洛阳）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小关系为（

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

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·江苏苏州）已知SKIPIF1<0，则SKIPIF1<0的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点五解不等式【例5-1】（2022·全国·高三专题练习）已知函数SKIPIF1<0，则不等式SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例5-2】（2022·浙江·舟山中学）已知函数SKIPIF1<0，若SKIPIF1<0都有SKIPIF1<0成立，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全国·高三专题练习）已知SKIPIF1<0（SKIPIF1<0为常数）为奇函数，则满足SKIPIF1<0的实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·山东）已知函数SKIPIF1<0，若对任意的SKIPIF1<0，都有SKIPIF1<0恒成立，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·全国·高三专题练习）设SKIPIF1<0，则SKIPIF1<0的解集为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考点六定点【例6】（2022·新疆阿勒泰）函数SKIPIF1<0图象过定点SKIPIF1<0，点SKIPIF1<0在直线SKIPIF1<0上，则SKIPIF1<0最小值为___________.【一隅三反】1．（2022·内蒙古）函数SKIPIF1<0的图象恒过定点SKIPIF1<0，若点SKIPIF1<0在直线SKIPIF1<0上，其中SKIPIF1<0