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1、26.1.2 反比例函数的图象和性质知能准备【学习目标】1、画反比例函数的图象，并知道该图象与正比例函数、一次函数图象的区别，能从反比例函数的图象上分析出简单的性质 2、能用反比例函数的定义和性质解决实际问题【学情分析】前面已经学习了一次函数和二次函数，对研究函数有了一定的方法；即画出图像并根据图像研究其性质【学思指导】教法：讲授法、对比法学法：类比 法、数形结合法学科素养：通过画图象，进一步培养“描点法”画图的能力和方法，并提高对函数图象的分析能力同时尝试用类比和特殊到一般的思路方法，归纳反比例函数一些性质特征【板书设计】302 反比例函数的图像和性质（一）画图：xy6画图：xy6性质步骤：
2、步骤：图像：图像：【课前预习】1 若 y=(21)(1)nnx是反比例函数，则 n 必须满足条件 n 12或 n-1 2用描点法画图象的步骤简单地说是列表、描点、连线 3试用描点法画出下列函数的图象：（1）y=2x；（2）y=1-2x设计意图：通过回忆，学会用描点法画函数的图象课堂引讨【展示互动】问题：我们已知道，一次函数y=kx+b（k0）的图象是一条直线，?那么反比例函数 y=kx（k 为常数且 k0）的图象是什么样呢？尝试用描点法来画出反比例函数的图象画出反比例函数 y=6x和 y=-6x的图象解：列表思考：取什么值更易描出来x-6-5-4-3-2-1 1 2 3 4 5 6 y=6x-
3、1-1.5-2-6 3 1 y=-6x1 1.2 3 6-1.5（请把表中空白处填好）描点，以表中各对应值为坐标，在直角坐标系中描出各点连线，用平滑的曲线把所描的点依次（从大到小或从小到大的顺序）连接起来探究反比例函数y=6x和 y=-6x的图象有什么共同特征？它们之间有什么关系？做一做把 y=6x和 y=-6x的图象放到同一坐标系中，观察一下，看它们是否对称归纳：反比例函数 y=6x和 y=-6x的图象的共同特征：（1）它们都由两条曲线组成（2）随着 x 的不断增大（或减小），曲线越来越接近坐标轴（x 轴、y 轴）（3）反比例函数的图象属于双曲线此外，y=6x的图象和 y=-6x的图象关于
4、x 轴对称，也关于 y 轴对称做一做在平面直角坐标系中画出反比例函数y=3x和 y=-3x的图象交流两个函数图象都用描点法画出？【分析】由 y=6x和 y=-6x的图象及 y=3x和 y=-3x的图象知道，（1）它们有什么共同特征和不同点？（2）每个函数的图象分别位于哪几个象限？（3）在每一个象限内，y 随 x 的变化而如何变化？猜想反比例函数y=kx（k0）的图象在哪些象限由什么因素决定？?在文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10
5、 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7
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7、 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5
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9、1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:
10、CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J
11、1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1每一个象限内，y 随 x 的变化情况如何？它可能与坐标轴相交吗？【归纳】（1）反比例函数 y=kx（k 为常数，k0）的图象是双曲线（2）当 k0 时，双曲线的两支分别位于第一、第三象限，在每个象限内，y?值随 x 值的增大而减小（3）当 k0时，下列图象中哪些可能是y=kx 与 y=kx（k0）在同一坐标系中的图象（）【分析】对于 y=kx 来说，当 k0 时，图象
12、经过一、三象限，当 k0 时，图象在一、三象限，当k 0，在图象的每一支上，y 值随 x 的增大而减小2下列图象中，是反比例函数的图象的是（D）3在反比例函数y=kx（kx20，则 y1-y2的值为（A）（A）正数（B）负数（C）非正数（D）非负数4已知反比例函数y=2kx的图象在第一、三象限内，则k 的值可是 _（写出满足条件的一个k 值即可）5在直角坐标系中，若一点的横坐标与纵坐标互为倒数，?则这点一定在函数图象上 y=1x（填函数关系式）6若一次函数y=kx+b 的图象经过第一、二、四象限，则反比例函数y=kbx的图象一定在二、四象限7两个不同的反比例函数的图象是否会相交？为什么？【答案
13、】不会相交，因为当k1k2时，方程1kx2kx无解8点 A（a，b）、B（a-1，c）均在反比例函数 y=1x的图象上，若 a0，则 b c【纠错补漏】【教学反思】文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8
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18、1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10
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20、编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8J1J1H6N10 HH8T7R6P5T3 ZI1N5R10O1S1文档编码:CC8
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