反比例函数综合复习：.pdf

1 反比例函数综合姓名一、反比例函数的概念：一般地，形如ykx(k 为常数，且k0)的函数称为反比例函数，其中x 是自变量，y 是 x 的函数，k是比例系数.注意：1、正比例函数为y=kx（k 是常数，且k0）；反比例函数可化为xy=k（k 是常数，且k0）；2、要求出反比例函数的解析式，只要求出k 即可；3、反比例函数的自变量x 的取值范围是不等于0 的一切实数；4、自变量 x 若乘以一个常数，仍然是反比例函数，但自变量x 加减一个常数，则不是反比例函数。二、反比例函数的图像与性质：反比例函数ykx的图像是有两支曲线组成的，这两支曲线称为双曲线.当 k0 时，两支曲线分别位于第一、三象限内；当 k 0)的图象上，且横坐标为2.若将点P先向右平移两个单位，再向上平移一个单位后所得的像为点P.则在第一象限内，经过点P的反比例函数图象的解析式是（）A)0(5xxyB.)0(5xxyC.)0(6xxyD.)0(6xxy7（2009 恩施市）一张正方形的纸片，剪去两个一样的小矩形得到一个“E”图案，如图所示，设小矩形的长和宽分别为x、y，剪去部分的面积为20，若210 x，则y与x的函数图象是（）8（2009 年兰州）如图，在直角坐标系中，点A是x轴正半轴上的一个定点，点B是双曲线3yx（0 x）上的一个动点，当点B的横坐标逐渐增大时，OAB的面积将会（）A逐渐增大 B不变C逐渐减小 D先增大后减小2 10 5 O x y 2 10 5 O x y 2 10 10 O x y 2 10 10 O x y y x 12 2 2 ABCD12 x y O A B A B O x y 文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F63 9（2009 泰安）如图，双曲线)0(kxky经过矩形QABC 的边 BC 的中点 E，交 AB 于点 D。若梯形ODBC 的面积为3，则双曲线的解析式为（）Axy1Bxy2Cxy3Dxy610、已知反比例函数0kykx的图象上有两点A（1x，1y），B（2x，2y），且12xx，则12yy（）A、正数 B、负数 C、非正数 D、不能确定11、已知112233(,),(,),(,)x yxyxy是反比例函数4yx的图象上三点，且1230 xxx，则123,y yy的大小关系是（）A、1230yyy B、1230yyy C、1320yyy D、1320yyy12、在同一坐标系中，函数kyx和3ykx的图象大致是（）二、填空题：1、(2009 年陕西)若 A(x1，y1)，B(x2，y2)是双曲线xy3上的两点，且x1x20，则 y1 y22、设反比例函数ykx1，(,)xy11、(,)xy22为其图象上的两点，若xx120时，yy12，则k的取值范围是 _ 3、已知反比例函数ykx图象与直线xy2和1xy的图象过同一点，则当x0 时，这个反比例函数值y随x的增大而 _（填增大或减小）；4、（2009 年河南）点 A(2，1)在反比例函数ykx的图像上，当 1x4 时，y的取值范围是 .5、（2009 年新疆）若梯形的下底长为x，上底长为下底长的13，高为y，面积为60，则y与x的函数关系是 _（不考虑x的取值范围）6、函数2xy和函数xy2的图像有个交点；7、已知函数xayaxy4和的图象有两个交点，其中一个交点的横坐标为1，则两个函数图象的交点坐标是；文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 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ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F64 y O x A C B x yA B O 1S2Sx y A O B 8.（2009 仙桃）如图，已知双曲线)0k(xky经过直角三角形OAB斜边 OB的中点 D，与直角边AB相交于点 C 若 OBC 的面积为3，则 k_9、（2009 年包头）如图，已知一次函数1yx的图象与反比例函数kyx的图象在第一象限相交于点A，与x轴相交于点CABx，轴于点B，AOB的面积为1，则AC的长为 _10、(2009 年牡丹江市)如图，点A、B是双曲线3yx上的点，分别经过A、B两点向x轴、y轴作垂线段，若1S阴影，则12SS三解答题1、如图，已知点A 是一次函数y=x 的图象与反比例函数的图象在第一象限内的交点，点B 在 x 轴的负半轴上且 OA=OB，AOB的面积为2.求反比例函数的解析式.2、如图，已知(4)An，(24)B，是一次函数ykxb的图象和反比例函数myx的图象的两个交点(1)求反比例函数和一次函数的解析式；(2)求直线AB与x轴的交点C的坐标及 AOB的面积；(3)求方程0 xmbkx的解；（请直接写出答案）(4)求不等式0 xmbkx的解集.（请直接写出答案）3、如图，已知直线12yx与双曲线(0)kykx交于AB，两点，且点A的横坐标为4（1）求k的值；（2）若双曲线(0)kykx上一点C的纵坐标为8，求AOC的面积；OxAyB文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F65 DxyBAOC4、如图正比例函数y=k1x 与反比例函数xky2交于点 A，从 A 向 x 轴、y 轴分别作垂线，所构成的正方形的面积为4。分别求出正比例函数与反比例函数的解析式。求出正、反比例函数图像的另外一个交点坐标。求 ODC 的面积。5、已知反比例函数xky2和一次函数y=2x-1，其中一次函数的图象经过（a,b），（a+1，b+k）两点.（1）求反比例函数的解析式；（2）如图，已知点 A在第一象限，且同时在上述两个函数的图象上，求点A的坐标；（3）利用（2）的结果，请问：在x 轴上是否存在点P，使 AOP为等腰三角形？若存在，把符合条件的P点坐标都求出来；若不存在，请说明理由.文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 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HY5Z7T9K5J2 ZP2V5J1A9F66 Ax y O Bx y O Cx y O Dx y O 反比例函数综合作业姓名1、若by与ax1成反比例，则y与x的函数关系式是（）A正比例；B反比例；C一次函数；D二次函数。2、已知反比例函数xy2，下列结论中，不正确的是（）A图象必经过点(1，2)By 随 x 的增大而减少C图象在第一、三象限内D若2,1yx则3、若()A ab，(2)B ac，两点均在函数1yx的图象上，且0a，则b与c的大小关系为（）AbcBbcCbcD无法判断4、已知反比例函数)0(kxky的图像上有两点A(1x，1y)，B(2x，2y)，且21xx，则21yy的值是（）A.正数；B负数；C非正数；D不能确定。5、函数yxm与(0)mymx在同一坐标系内的图象可以是（）6、如图，已知函数kyx中，0 x时，y随x的增大而增大，则ykxk的大致图象为（）7、在同一平面直角坐标系中，正比例函数y=(m-1)x与反比例函数xmy4的图像的大体位置不可能是（）8、如图,一次函数1=1 与反比例函数2=x2的图像交于点A(2,1),B(1,2),则使12的的取值范围是（）A.2 B.2 或 1 0 C.1 2 D.2 或 1 x y O Ax y O Bx y O Cx y O DO B A文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 ZP2V5J1A9F6文档编码:CJ2I7X8C1U9 HY5Z7T9K5J2 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