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1、反比例函数知识点归纳总结与典型例题（一）反比例函数的概念：知识要点：1、一般地，形如 y=xk(k是常数,k=0)的函数叫做反比例函数。注意：（1）常数 k 称为比例系数，k 是非零常数；（2）解析式有三种常见的表达形式：（A）y=xk（k 0），（B）xy=k（k 0）（C）y=kx-1（k0）例题讲解：有关反比例函数的解析式（1）下列函数，1)2(yx.11xy21xy.xy212xy13yx；其中是y关于 x 的反比例函数的有：_。（2）函数22)2(axay是反比例函数，则a的值是（）A 1 B 2 C2 D2 或 2（3）若函数11mxy(m是常数)是反比例函数，则m_，解析式为 _
2、（4）反比例函数(0kykx）的图象经过（2，5）和（2，n），求 1）n的值；2）判断点B（24，2）是否在这个函数图象上，并说明理由(二)反比例函数的图象和性质：知识要点：1、形状：图象是双曲线。2、位置：（1）当 k0 时,双曲线分别位于第_象限内；（2）当 k0 时,_,y随 x 的增大而 _；（2）当 k0 时,_,y随 x 的增大而 _。4、变化趋势：双曲线无限接近于x、y 轴,但永远不会与坐标轴相交5、对称性：（1）对于双曲线本身来说，它的两个分支关于直角坐标系原点_；（2）对于 k 取互为相反数的两个反比例函数（如：y=x6和 y=x6）来说，它们是关于x 轴，y 轴 _。例题
3、讲解：反比例函数的图象和性质：（1）写出一个反比例函数，使它的图象经过第二、四象限（2）若反比例函数22)12(mxmy的图象在第二、四象限，则m的值是（）A、1 或 1;B、小于12的任意实数;C、1;、不能确定（3）下列函数中，当0 x时，y随x的增大而增大的是（）A34yxB123yxC4yxD12yx（4）已知反比例函数2yx的图象上有两点A（1x，1y），B（2x，2y），且12xx，则12yy的值是（）A正数B负数C非正数D不能确定（5）若点（1x，1y）、（2x，2y）和（3x，3y）分别在反比例函数2yx的图象上，且1230 xxx，则下列判断中正确的是（）A123yyyB31
4、2yyyC231yyyD321yyy（6）在反比例函数xky1的图象上有两点11()xy，和22()xy，若xx120时，yy12，则k的取值范围是（7）老师给出一个函数,甲、乙、丙三位同学分别指出了这个函数的一个性质:甲:函数的图象经过第二象限;乙:函数的图象经过第四象限;丙:在每个象限内,y 随 x 的增大而增大.请你根据他们的叙述构造满足上述性质的一个函数:.（三）反比例函数与面积结合题型。知识要点：1、反比例函数与矩形面积：若P(x，y)为反比例函数xky(k0)图像上的任意一点如图1 所示，过P作PMx轴于M，作PNy轴于N，求矩形PMON的面积.分析：S矩形PMON=xyxyPNP
5、Mxky,xy=k,S=k.2、反比例函数与矩形面积：若Q(x，y)为反比例函数xky(k0)图像上的任意一点如图2 所示，过Q作QAx轴于A(或作QBy轴于B)，连结QO，则所得三角形的面积为：SQOA=2k（或SQOB=2k）.说明：以上结论与点在反比例函数图像上的位置无关.（1）如图 3，在反比例函数xy6（x 0）的图象上任取一点P，过P点分别作x轴、y轴的垂线，垂足分别为M、N，那么四边形PMON的面积为P y x O M N 图 1 O B y x A Q 图P y M x 0 N 3 文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ
6、10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL
7、3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2
8、G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:
9、CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6
10、HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 Z
11、N2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编
12、码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4M y N x O 图 4（2）反比例函数xky的图象如图4 所示，点M是该函数图象上一点，MNx轴，垂足为N.如果SMON=2，这个反比例函数的解析式为_(3)如图 5，正比例函数(0)ykx k与反比例函数2yx的图象相交于A、C两点，过点 A作 AB x轴于点 B，连结 BC 则 ABC的面积等于（）A1 B2 C 4 D随k的取值改变而改变（4）如图
13、 6，A、B是函数2yx的图象上关于原点对称的任意两点，BCx轴，ACy轴，ABC的面积记为S，则（）A2S B 4SC24SD4S（5）如图7，过y轴正半轴上的任意一点P，作x轴的平行线，分别与反比例函数xyxy24和的图象交于点A和点B，若点C是x轴上任意一点，连接AC、BC，则ABC的面积为（）(四)一次函数与反比例函数(1)一次函数y=2x+1 和反比例函数y=的大致图象是（）A B C D(2)一次函数)0(kkkxy和反比例函数)0(kxky在同一直角坐标系中的图象大致是()yxO A C B 图 6 图 5 图 7 文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN
14、2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码
15、:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6
16、 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5
17、ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档
18、编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6
19、L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L
20、5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4（3）一次函数y1=k1x+b 和反比例函数y2=（k1?k20）的图象如图所示，若y1 y2，则 x 的取值范围是（）A、2x0 或 x1 B、2x1C、x 2 或 x1 D、x 2 或 0 x1（4）正比例函数2xy和反比例函数2yx的图象有个交点（5）正比例函数y=k1x(k1 0)和反比例函数y=2kx(k20)的一个
21、交点为(m,n),则另一个交点为_.（6）设函数y=2x与y=x1 的图象的交点坐标为（a，B），则11ab的值为(7)如图，RtABO的顶点 A是双曲线kyx与直线yxm?在第二象限的交点，AB垂直x轴于 B，且 SABO32，则反比例函数的解析式(8)若反比例函数xky与一次函数y3xb都经过点(1，4)，则kb_（9）如图，已知A（4，a），B（2，4）是一次函数ykxb的图象和反比例函数yxm的图象的交点（1）求反比例函数和一次函数的解祈式；（2）求A0B的面积(10)如图,在平面直角坐标系中，直线2kyx与双曲线kyx在第一象限交于点A，与x轴交于点C，AB x轴，垂足为B，且AOB
22、S1求：（1）求两个函数解析式；（2）求 ABC的面积（第（7）题）2kx文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6
23、 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5
24、ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档
25、编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6
26、L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L
27、5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4
28、文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4（11）平面直角坐标系中，直线AB交 x 轴于点 A，交 y 轴于点 B 且与反比例函数图象分别交于C、D两点，过点 C作 CM x轴于 M，AO=6，BO=3，CM=5 求直线 AB的解析
29、式和反比例函数解析式文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编
30、码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L
31、6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5
32、 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文
33、档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E
34、6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4文档编码:CJ10Q8F8E6L6 HL3Y5B1D2L5 ZN2G1H7B3D4