幂函数复习讲义.doc

<p><span id="_baidu_bookmark_start_0" style="display: none; line-height: 0px;">‍</span>例1、定义在R上得函数满足,当时,
.
(1) 求得值;
(2) 比较与得大小.
例2.方程lgx+x=3得解所在区间为(　　　 )
A.(0,1) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;B.(1,2) &nbsp; C.(2,3) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;D.(3,+∞)
例3、设a＞0, f (x)＝就是R上得奇函数、
(1) 求a得值;
(2) 试判断f (x )得反函数f－1 (x)得奇偶性与单调性、
例4、 就是否存在实数a, 使函数f (x )＝在区间上就是增函数? 如果存在,
说明a可以取哪些值; 如果不存在, 请说明理由、
例5.定义在R上得单调函数f(x)满足f(3)=log3且对任意x,y∈R都有f(x+y)=f(x)+f(y).
(1)求证f(x)为奇函数;
(2)若f(k·3)+f(3-9-2)＜0对任意x∈R恒成立,求实数k得取值范围.
1、若函数(,且)得图像经过二、三、四象限,则一定有( &nbsp; &nbsp;)
A、且 &nbsp; &nbsp; B、且 &nbsp; &nbsp; C、且 &nbsp; &nbsp; D、且
y
x
0
1
1
y
x
0
1
1
-1
y
x
0
1
1
y
x
0
1
1
2、函数得图像就是( &nbsp; &nbsp;)
&nbsp; &nbsp; A &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; B &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; C &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; D、
3、方程得解x =_______、
4、,则、
5若,,则________、
6已知函数,若,则、
、
(1);(2);(3);(4);(5).

(1)所有得幂函数在(0,+∞)都有定义,并且图象都过点(1,1);
(2)时,幂函数得图象通过原点,并且在区间上就是增函数.特别地,当时,幂函数得图象下凸;当时,幂函数得图象上凸;
(3)时,幂函数得图象在区间上就是减函数.在第一象限内,当从右边趋向原点时,图象在轴右方无限地逼近轴正半轴,当趋于时,图象在轴上方无限地逼近轴正半轴.
规律1:在第一象限,作直线,它同各幂函数图象相交,按交点从下到上得顺序,幂指数按从小到大得顺序排列.
规律2:幂指数互为倒数得幂函数在第一象限内得图象关于直线对称.
定义域 、值域 、奇偶性 、 单调性 、 定点。
1.就是偶函数,且在就是减函数,则整数得值就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; .
2.函数得定义域就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; .
3.函数就是幂函数,且在上就是减函数,则实数______、
1、 数得定义域就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
A &nbsp; [0,+∞] &nbsp; B &nbsp;(—∞,0) &nbsp; C &nbsp;(0,+∞) &nbsp; D &nbsp; R
2、 数得图象就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;( &nbsp; &nbsp; )
y &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y
O &nbsp; &nbsp; &nbsp;x &nbsp; &nbsp; &nbsp; &nbsp;O &nbsp; &nbsp;x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; O &nbsp; &nbsp; x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; O &nbsp; &nbsp; x
3、 下列函数中就是偶函数得就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
A &nbsp; &nbsp; &nbsp;B &nbsp; &nbsp;C &nbsp; &nbsp; D &nbsp;
4、 幂函数,其中m∈N,且在(0,+∞)上就是减函数,又,则m=
A &nbsp; 0 &nbsp; &nbsp; B &nbsp; &nbsp; 1 &nbsp; &nbsp; C &nbsp; 2 &nbsp; &nbsp; &nbsp; D &nbsp; &nbsp; &nbsp; &nbsp;3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
5、若幂函数得图象在0&lt;x&lt;1时位于直线y=x得下方,则实数a得取值范围就是
A &nbsp; &nbsp;a&lt;1 b=&quot;&quot; a=&quot;&quot;&gt;1 &nbsp; &nbsp; C &nbsp; &nbsp;0&lt;a&lt;1 &nbsp; &nbsp; D &nbsp; &nbsp;a&lt;0 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;( &nbsp; &nbsp; )
6、 列结论中正确得个数有 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;( &nbsp; &nbsp; )
(1)幂函数得图象一定过原点 &nbsp; (2) 当a&lt;0时、,幂函数就是减函数, a=&quot;&quot;&gt;0时,幂函数就是增函数 &nbsp;(4)函数既就是二次函数,又就是幂函数
A &nbsp;0 &nbsp; B &nbsp; &nbsp;1 &nbsp; &nbsp;C &nbsp;2 &nbsp; &nbsp;D &nbsp;3
7、若x∈(8,10),则化简得 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
A &nbsp;2x-18 &nbsp; &nbsp; B &nbsp;2 &nbsp; &nbsp; &nbsp;C &nbsp;18-2x &nbsp; &nbsp; &nbsp;D &nbsp; -2
8、 个数,,得大小顺序就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;( &nbsp; &nbsp; )
A &nbsp;c&lt;a&lt;b &nbsp; &nbsp;B &nbsp; c&lt;b&lt;a &nbsp; &nbsp; C &nbsp; a&lt;b&lt;c &nbsp; &nbsp; &nbsp; D &nbsp; b&lt;a&lt;c
9、等于 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
A &nbsp; &nbsp; &nbsp;B &nbsp; &nbsp; &nbsp; C &nbsp; &nbsp; &nbsp; D &nbsp; &nbsp;
10、已知,那么= &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
A &nbsp; &nbsp; &nbsp; &nbsp; B &nbsp;8 &nbsp; &nbsp; &nbsp; C &nbsp; 18 &nbsp; &nbsp; &nbsp; &nbsp;D &nbsp; &nbsp;
11、若幂函数存在反函数,且反函数得图象经过则得表达式为
A &nbsp; &nbsp; &nbsp;B &nbsp; &nbsp; C &nbsp; &nbsp; &nbsp;D &nbsp; &nbsp; ( &nbsp; &nbsp; )
12、若,则等于 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ( &nbsp; &nbsp; )
A &nbsp; &nbsp; &nbsp; &nbsp;B &nbsp; &nbsp; &nbsp;C &nbsp; &nbsp; &nbsp; &nbsp; D &nbsp; &nbsp;
二、填空题(每题5分,共25分)
13、函数得定义域就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
14、设就是定义在R上得奇函数,当时,,则= &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
15、若,则实数a得取值范围就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
16、方程得解得个数就是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
(填“增”或“减”)

17、函数得对称中心就是 &nbsp; &nbsp; &nbsp; &nbsp;,在区间 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;就是 &nbsp; &nbsp; 函数
三、解答题(每题9分,共27分)
20、求函数在得最值,并给出最值时对应得x得值。
例1.已知函数,当 为何值时,:
（1） 就是幂函数;(2)就是幂函数,且就是上得增函数;(3)就是正比例函数;(4)就是反比例函数;(5)就是二次函数;
例2.比较大小:
(1) &nbsp;(2)(3)(4)
一、 分类讨论得思想
例3.已知幂函数()得图象与轴、轴都无交点,且关于原点对称,求得值.
例4、设函数f(x)＝x3,
　　(1)求它得反函数;
　　(2)分别求出f－1(x)＝f(x),f－1(x)＞f(x),f－1(x)＜f(x)得实数x得范围.
例5、求函数y＝＋2x＋4(x≥－32)值域.
二、数形结合得思想
例1 　已知点在幂函数得图象上,点,在幂函数得图象上.
问当x为何值时有:(１);(２);(３)
例2 　函数得定义域就是全体实数,则实数m得取值范围就是(　　).
例3 　已知函数为偶函数,且,求m得值,并确定得解析式.
例4 已知函数,设函数,问就是否存在实数,使得在区间就是减函数,且在区间上就是增函数？若存在,请求出来;若不存在,请说明理由.
例5 　讨论函数在时随着x得增大其函数值得变化情况.
例1 若,试求实数m得取值范围.
例2 　例2　若,试求实数m得取值范围.
例3 　例3若,试求实数m得取值范围.
例4 　例4　若,试求实数m得取值范围.</p><!--0时、,幂函数就是减函数,--><!--1-->