幂函数、指(对)数函数

幂函数、指(对)数函数【复习指导】1.是幂函数时必须;在上是增函数;上是减函数.用幂函数的单调性比较两指数式的大小时,要化为同次幂.2.是增函数是减函数.用指(对)数函数的单调性比较两个指(对)式的大小时，要化为同底。3.把握幂函数、指(对)数函数的图象特征,并与单调性结合起来加以应用.4.注意估计数值的大小,特别是正、负,大于1还是小于1.一：函数性质〖练习1〗解析式与定义域（基本题）01．某工厂产量的月增长率为；则当年月份的产量比月份的产量的增长率为02．函数，对于任意正实数都有03．若指数函数的反函数过点；则此指数函数是04．若函数的反函数的图象必过定点05．函数的定义域是06．已知点在函数的图象上；则函数的定义域为07．定义在上的奇函数满足，当时，；则， 〖练习2〗值域（基本题-中等题）08．函数的值域是09．要使函数的值域为；则10．下列函数中，值域为的是11．已知函数.求的最值.12．设，当（1）、;（2）的解集为；求;（3）集合；求 〖练习3〗奇偶性与对称性（中等题）13．已知函数，若；则14．已知是偶函数；则的图象关于对称轴轴直线原点15．函数关于直线对称；则16．设；则函数和的图象关于对称；函数和的图象关于对称17．当时，函数和函数的图象关于对称轴轴直线直线18．设指数函数的反函数依次为；若则、的图象位置关系是关于直线对称关于原点对称关于轴对称关于轴对称 〖练习4〗函数图象（中等题）19．将的图象再作关于直线对称的图象，可得到的图象先向左平行移动个单位先向右平行移动个单位先向上平行移动个单位先向下平行移动个单位20．函数的图象如右图，它在定义域上单调递减给出下列四个结论：①②③④其中正确结论的个数是21．方程的解共有个22．方程的实数根的个数是个23．（1）方程有两相异实数根；求（2）方程有两相异实数根；求（3）方程仅有一不同实数根；求23．已知方程的解为，方程的解为；则24．已知方程的实数根为，的实数根为，的实数根为；则的大小顺序是※25．已知函数，当时，有；则正确的结论是 〖练习5〗单调性（中等题）26．下列函数中，在区间上是增函数的是27．如果函数在上是减函数；则28．已知，若时，；则是增函数减函数奇函数偶函数29．函数的单调递增区间是30．已知函数在区间上是减函数；则31．设；则下列不等式中不正确的是32．已知，在区间上的函数值总小于；则※33．已知函数的定义域为；则 〖练习6〗综合题34．函数的图象与的图象关于直线对称；则函数的递增区间是35．函数的值域是；单调减区间是36．已知关于的方程有一根是；则这个方程的其余根是37．对于给定的函数；有下列四个结论：①的图象关于原点对称②在上是增函数③④有最小值其中正确结论的序号是38．已知函数（1）求的定义域（2）讨论的奇偶性（3）讨论的单调性（4）求的反函数 二：指(对)数方程〖练习11〗(基本题)解下列方程39．方程的解为；40．方程的解为；41．方程的解为；42．方程的解为；○小结：43．方程的解为；44．方程的解为；45．方程的解为；46．方程的解为；47．方程的解为；※48．方程的解为； 三:比较大小方法一:函数的单调性〖练习1〗比较下列数的大小01．02．03．04．05．06．方法二：间接法中间函数及中间数(0,)〖练习2〗(提高题)07．当满足何条件时○小结：08．比较下列数的大小（1）（2） 09．已知；试比较的大小.10．已知；试比较的大小.11．已知；则※12．已知；则13．已知；则四：图象及最值〖练习3〗（基本题）14．已知()的图象经过第一、二、三象限；则、15．的图象与的图象关于轴对称;则之间关系是16．的图象与的图象关于轴对称;则之间关系是17．的图象与的图象关于轴对称;则之间关系是18．的图象与的图象关于轴对称;则之间关系是 19．在下列图象中，二次函数与指数函数的图象只可能是〖练习4〗（提高题）20．如果在上恒有;则。21．已知内恒有；则判断上的单调性.22．已知在上是的减函数.则23．已知上是减函数;则. 〖练习5〗(提高题)24．已知恒有;则.25．（1）已知的最大值比最小值大;则.※（2）又如何？※（3）又如何？26．设；则的最大值是;27．求函数的最小值. 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