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1、指数函数知识点总结（一）指数与指数幂的运算1根式的概念：一般地，如果，那么叫做的次方根，其中1，且*负数没有偶次方根；0 的任何次方根都是0，记作。当是奇数时，当是偶数时，2分数指数幂正数的分数指数幂的意义，规定：，0 的正分数指数幂等于0，0 的负分数指数幂没有意义3实数指数幂的运算性质（1）；（2）；（3）（二）指数函数及其性质1、指数函数的概念：一般地，函数叫做指数函数，其中x 是自变量，函数的定义域为R注意：指数函数的底数的取值范围，底数不能是负数、零和12、指数函数的图象和性质a1 0a1（0a0（x0)个单位,则得到函数y ax+b的图像;把函数 yax文档编码:CY4J6I9W2
2、R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9
3、L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2
4、R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9
5、L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2
6、R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9
7、L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2
8、R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3的图像向右平移b（b0)个单位,则得到函数yax-b的图像；把函数yax的图像向上平移b（b0)个单位,则得到函数yax+b 的图像;把函数 yax的图像向下平移b（b0)个单位,则得到函数yaxb 的图像（左加右减，上加下减）（2）对称变换：函数yax的图像与函数ya-x的图像关于y 轴对称；函数y-ax的图像与函数yax的图像关于x 轴对称；函数y-a-x的图像与函数yax的图像关
9、于原点对称；函数ya|x|的图像关于y轴对称.例:为了得到函数935xy的图象，可以把函数3xy的图象（）A 向左平移9 个单位长度，再向上平移5 个单位长度B 向右平移9 个单位长度，再向下平移5 个单位长度C 向左平移2 个单位长度，再向上平移5 个单位长度D 向右平移2 个单位长度，再向下平移5 个单位长度分析：注意先将函数935xy转化为235xt，再利用图象的平移规律进行判断解：293535xxy，把函数3xy的图象向左平移2 个单位长度，再向上平移5 个单位长度，可得到函数935xy的图象，故选（C）评注：用函数图象解决问题是中学数学的重要方法，利用其直观性实现数形结合解题，所以要
10、熟悉基本函数的图象，并掌握图象的变化规律，比如：平移、伸缩、对称等比较两个有理数指数幂的大小：（1）比较幂的大小常用方法：比差（商）法；函数单调性法；中间值法：要比较A与 B 的大小，先找一个中间值C，在比较A与 C，B与 C的大小，由不等式的传递性得到A与 B的大小；（2）用指数函数单调性比较大小，基本步骤：确定所要考察的指数函数；根据底数情况指出已确定的指数函数的单调性；比较指数的大小，利用指数函数单调性得出同底数幂的大小关系.（3）常用技巧：对于底数相同、指数不同的两个幂的大小比较，可利用指数函数单调性判断；对于底数不同，指数相同的两个幂的大小比较，可利用指数函数图像变化规律来判断；对于
11、底数不同指数也不同的两个幂的大小比较，则应通过中间量来比较；对于3 个或以上的数的大小比较，则应先根据值的大小（特别是与0、1 的大小）进行分组，在比较各组数的大小即可.（4）异底指数比较大小的五种技巧：化同底：因为化为同底后即可应用指数函数单调性解决，所以能化同底的尽可能化；商比法：不同底但可以化为同指数的两数比较大小，用商比法即可，这时要注意分母的正负；例:比较下列两数大小：1.1-0.2和 1.3-0.1。文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9
12、W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7
13、J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9
14、W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7
15、J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9
16、W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7
17、J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9
18、W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3取中间值：不同底也不同指数宜先与中间值0、1 比较大小，在间接得解；估算法：大致估算数值；图解法：借助图像例：比较下列各组数的大小：（1）若，比较与；（2）若，比较与；（3）若，且，比较a与b；（4）若，且，比较a与b解：（1）由，故又，故从而（2）由，因，故又，故从而（3）应有因若，则又，故，这样又因，故从而，这与已知矛盾（4）应有 因若，则 又，故，这样有 又因，且，故从而，这与已知矛盾小结：比较通常借助相应函数的单调性、奇偶性、图象来求解例：曲线分别是指数函数,和的图象,则与 1 的大小关系是().(分 析:首先可以根据指数函数单调
19、性,确定,在轴右侧令文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6
20、I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 Z
21、H7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6
22、I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 Z
23、H7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6
24、I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 Z
25、H7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3,对应的函数值由小到大依次为,故应选.小结:这种类型题目是比较典型的数形结合的题目,第(1)题是由数到形的转化,第(2)题则是由图到数的翻译,它的主要目的是提高学生识图,用图的意识.例：将下列各数从小到大排列起来.35322-6523523,533231-31-303221212131-），（），（），（），（），（），（），（）（与指数
26、函数相关的定义域值域问题：（1）求由指数函数构成的复合函数的定义域时，可能涉及解指数不等式（即未知数在指数上的不等式）解指数不等式的基本方法是把不等式两边化为同底数幂的形式，利用函数单调性去幂的形式；（2）求定义域方法：yaf(x)的定义域与函数y=f(x)的定义域相同；y=f(ax)的定义域与函数y=f(x)的定义域不一定相同，求其定定义域时，应通过复合函数定义由f(x)的定义域与g(x)=ax的值域的等价性，建立关于x 的不等式，利用指数函数相关性质求解.（3）求值域方法：求 yaf(x)的值域时，先求函数y=f(x)的值域，再根据指数函数单调性确定函数yaf(x)的值域；求 y=f(ax
27、)的值域时，可用换元法求解，但换元后应注意引入新变量的取值范围；（4）几种基本形式的的定义域与值域问题：形如 y af(x)的函数的定义域就是y=f(x)的定义域；形如 yaf(x)的函数的值域，应该先求出f(x)的值域，再由单调性求出值域，若a 范围不确定，则需对a论进行讨论；形如求 y=f(ax)的值域，要先求出u=ax的值域，再结合y=f(u)确定出值域.例求函数216xy的定义域和值域文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6
28、P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档
29、编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6
30、P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档
31、编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6
32、P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档
33、编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6
34、P1M9M7 ZH7J9L7J7F3解：由题意可得2160 x，即261x，20 x，故2x,函数()f x 的定义域是2，令26xt，则1yt，又2x，20 x 2061x，即 01t 011t，即01y,函数的值域是01，评注：利用指数函数的单调性求值域时，要注意定义域对它的影响练习 1：已知-1x2,求函数 f(x)=3+2 3x+1-9x的最大值和最小值解：设 t=3x,因为-1 x2，所以931t，且 f(x)=g(t)=-(t-3)2+12,故当 t=3 即 x=1 时，f(x)取最大值12；当 t=9 即 x=2 时 f(x)取最小值-24。练习 2：已知函数（且）（1）求的最小
35、值；（2）若，求的取值范围解：（1），当即时，有最小值为（2），解得当时，；当时，例：已知，求函数的值域解：由得，即，解 之 得，于 是，即，故所求函数的值域为指数型复合函数单调性：判断形如y=af(x)（a0 且 a 不等于 1）的函数单调性方法：1、利用单调性定义，取值-作差-变形-定号.2、利用复合函数单调性：令 u=f(x),xnm,复合的两个函数y=au与 u=f(x)的单调性如果相同，则复合后的函数y=af(x)在上是增函数；若两者单调性相反，则其在定义域上是减函数.例：讨论函数xxxf22)51()(的单调性，并求其值域.nm,文档编码:CY4J6I9W2R9 HU1Y6P1M9
36、M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:C
37、Y4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9
38、M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:C
39、Y4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9
40、M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:C
41、Y4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9
42、M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3例：求函数 y23231xx的单调区间.分析这是复合函数求单调区间的问题可设 yu31,u x2-3x+2，其中 yu31为减函数u x2-3x+2 的减区间就是原函数的增区间(即减减增)ux2-3x+2 的增区间就是原函数的减区间(即减、增减)解：设 yu31,u x2-3x+2,y关于 u 递减，当 x(-，23)时，u 为减函数，y 关于 x 为增函数；当 x23，+)时，u 为增函数，y 关于 x 为
43、减函数.例:求函数xxy4212的单调区间.文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7
44、F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 H
45、U1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7
46、F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 H
47、U1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7
48、F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 H
49、U1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3指数函数综合应用：与奇偶性结合例：设 a0，f(x）=xxeaae是定义在R上的偶函数.（1）求 a 的值.（2）证明 f(x)在（0，）上是增函数.练习：若函数1212)(xxaaxf为奇函数.(1)确定 a 的值；（2）求函数f(x)的定义域；（3）求函数f(x)的值域；（4）讨论 f(x)单调性.练习：已知函
50、数2()()21xf xaaR，（1）求证：对任何,()aR f x为增函数；（2）若()f x为奇函数时，求a 的值。文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3文档编码:CY4J6I9W2R9 HU1Y6P1M9M7 ZH7J9L7J7F3