2021年高中数学毕业会考函数复习资料.pdf
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1、函数一、函数()yf x及有关性质。1.函数定义:()yf x中,自变量x的取值范围为函数的定义域。当xa时,()yf a叫函数值。所有函数值的集合叫做函数的值域。2.映射的定义::fAB两个允许:两个不允许:3.同一函数:_相同。_相同。值域相同。(可由得)4.函数定义域求法:使函数有意义的条件。整式函数(一次函数、二次函数)定义域为R。分式函数的分母不为0。偶次根式函数,被开放数大于或等于0。(()f x的()0f x)对数函数的底数大于0 且不等于1,真数大于0。有多个限制条件的转化为不等式组求定义域。5.函数的单调性:定义:逆运用:当()yf x在区间 m,n上为增函数时,若()()f
2、xf g x则有:()()()()xg xxng xm当()yf x在区间 m,n上为减函数时,若()()fxf g x则有:()()()()xg xxmg xn常用函数的单调性:.一次函数ykxb,当0k时为增函数;当0k时为减函数。.二次函数2yaxbxc,当0a时在(,2ba为减函数;在,)2ba为增函数。当0a时在(,2ba为增函数;在,)2ba为减函数。与开口方向和对称轴有关。.反比例函数1yx在,00与,上均为减函数;1yx在,00与,上均为增函数。.xya01aa且,当01a时为减函数;当1a时为增函数。.logayx01aa且,01a时,在0,上为减函数;当1a时,在0,上为增
3、函数。6.反函数:求函数()yf x的反函数的方法:|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页,共 9 页(1)先根据原函数的定义域求出其值域(2)由()yfx解出()xy(3)将()xy中的,x y互换,即得反函数1()yfx标明定义域有关性质:(1)原函数()yf x与反函数1()yfx的定义域和值域正好互换,原函数过点,a b,则反函数过点,b a。(2)互为反函数的图象关于yx成轴对称图形。(3)原函数与反函数的单调性相同。7.函数得奇偶性:存在奇偶性得条件时定义域必须关于原点对称,在定义域内,将xx换成后(1)若()()fx
4、fx,则()yf x为偶函数。(2)若()()fxf x,则()yf x为奇函数。有关性质:(1)偶函数得图象关于y轴对称,在对称区间上的单调性相反。(2)奇函数得图象关于原点对称,在对称区间上的单调性相同。8.求函数值域的基本方法(1)利用函数的单调性求值域:若()yf x在,m n上为增函数则其值域为(),()f mf n若()yf x在,m n上为减函数则其值域为(),()f nf m。(2)配方法:二次函数2224()24bacbyaxbxca xaaxR当0a时,有最小值244acba,值域为244acba,;当0a时,有最大值244acba,24,4acba。(3)反表示法:即利用
5、反函数的定义域既为原函数的值域。例如:求2121xxy的值域。(4)换原法:还原注意新元素的范围。例如:求1yxx的值域。(5)判别式法:形如:21112a xb xcyaxbxc类型,可转化为关于x的一元二次方程有解,0求值域。(6)图象法。9.周期性:若函数()yf x对于最小正周期T,使()()f xTf x,则称T为函数()yf x的最小正周期。|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页,共 9 页文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H1
6、0O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2
7、Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L
8、2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8
9、H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3
10、C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG
11、8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6
12、O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J310.对称性:若()()f txf tx则称xt为()yf x的对称轴二、指数函数与对数函数(一)指数1 根式与分数指数幂:nanmapa=1pa运算法则:mnaamnaanmamabmab()nnanna2 指数函数的图象和性质:xya01aa且xya1axya01a3 指数方程:(1)()()()()fxg xaaf xg x(化成底数相等)(2)2()0 xxaman可换元后求解,令x
13、ta(0)t4 指数复合函数的单调性:()u xya(1)01a时,()()u xyau x与的单调性相反(2)1a时,()()u xyau x与的单调性相同(一致)(二)对数函数1 对数式与指数式互化:logbaaNNb;log 1alogaalognaa2 对数的运算法则:loglogaaMNloglogaaMNlognaMlognam对数恒等式:logaNa图象性质定义域值域定 点单调性增函数减函数|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页,共 9 页文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4
14、J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U
15、6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H1
16、0O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2
17、Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L
18、2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8
19、H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3
20、C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3换底公式:logloglgcabbalogmab11logab1logab3 对数函数logayx01aa且的图象和性质logayx1alogayx01a(1)当a与b都大于 1 或都小于 1 时,log0ab(2)当a与b一个大于1 另一个小于1 时,log0ab4 对数方程:()()log()log()()0()0aafxg xf xg
21、 xf xg x四 图象变换,设0,0ab1.平移:()(),()()aayf xyf xayf xyf xa向右平移个单位向左平移个单位2.()(),()()byf xyf xb yf xyf xb向上平移 b个单位向下平移个单位3.对称:()(),()()xyyf xyf x yf xyfx关于 轴对称关于轴对称()()yf xyfx关于原点对称图象性质定义域值域定 点单调性增函数减函数|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页,共 9 页文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:
22、CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 H
23、C6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 Z
24、C5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编
25、码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7 HC6O8H10O1G7 ZC5U3C2Y4J3文档编码:CG8L2U6L7Y7
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