2022年2018春人教版数学九年级下册26.1.1《反比例函数》教案 .pdf

名师精编优秀教案第二十六章反比例函数26.1反比例函数26.1.1反比例函数教学目标知识技能1结合具体情境体会反比例函数的意义，丰富对函数、函数概念的认识和理解2能辨析一个函数是否为反比例函数，能根据已知条件确定反比例函数的解析式数学思考与问题解决1让学生经历从实际问题中抽象出反比例函数模型的过程，体会反比例函数来源于实际问题2能运用类比思想方法，从实际问题中抽象概括出反比例函数的概念，进一步感受待定系数法，确定反比例函数的解析式，丰富认识和理解数学概念的基本思路和方法情感态度经历反比例函数的形成过程，体验反比例函数也是描述变量间对应关系的重要数学模型，体会数学来源于生活，又服务于生活，培养学生良好的思考习惯和探索精神重点难点重点：理解反比例函数的概念，确定反比例函数的解析式难点：反比例函数意义的理解教学设计活动一：创设情境在下列实际问题中，变量间的对应关系具有函数关系吗？请写出它们的解析式1小明以6 km/h 的速度步行上学，他与家的距离S(单位：km)随时间 t(单位：h)的变化而变化(S6t)2小明家距学校2 km，他上学的步行速度v(单位：km/h)随时间 t(单位：h)的变化而变化(v2t)名师精编优秀教案思考：1.以上函数都是我们已学过的函数吗？它们有什么不同？2完成教材第2 页思考(1)(3)答案：(1)v1 463t；(2)y1 000 x；(3)S1.68104n.3上述与(1)(2)(3)具有怎样的共同特点？能否用一个函数解析式把它们表示出来？设计意图：利用学生熟悉的实际问题引入，提高学生思考问题的主动性和解决问题的能力，调动学生的学习兴趣，培养学生的模型思想，通过对这些问题的探究、观察分析，结合与同学的交流合作，对比已学过的正比例函数，找出新函数的特点，把握反比例函数的特征，从而促成反比例函数概念的生成活动二：生成概念归纳概括反比例函数的概念：一般地，形如 _()的函数，叫做反比例函数，其中x 是自变量，y 是函数，自变量 x 的取值范围是 _观察反比例函数的解析式，与正比例函数ykx(k 0)比较，并思考：1 两者从形式上有何异同？反比例函数ykx(k0)中，自变量的次数是1 吗？为什么？2反比例函数ykx(k0)中常数 k 的条件要求是什么？如何确定常数k?3反比例函数ykx(k0)中，两个变量的取值范围是什么？4反比例函数的解析式还有其他表达形式吗？5你能举出生活中类似的例子吗？试一试：下列关系式中，y 是 x 的反比例函数的是_(1)y1x；(2)yx2；(3)y9x1；(4)xy6；(5)y65x；(6)y2x1；(7)yx4；(8)y7x1.活动三：运用概念探究 1：当 a 取什么值时，函数y(a2)x|a|3是反比例函数？分析：由反比例函数的意义可知成为反比例函数需满足两个条件：(1)常数 k0；(2)自变量 x 的次数为 1.解：由题意得|a|3 1，a 20，解得 a 2，即 a 2 时，y(a2)x|a|3是反比例函数文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 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ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3名师精编优秀教案设计意图：掌握反比例函数的一般形式及其条件，特别是常数k 0 这个条件，往往容易忽略，学生通过对此问题的探究分析，小组成员间的交流，针对出现a2 和 a 2两种结果展开讨论，进一步加深对反比例函数概念的理解探究 2：教材第3 页例 1.分析：类比求一次函数解析式的过程，显然要运用待定系数法，先设出解析式，再根据已知条件求出待定系数变式：若反比例函数ykx与一次函数yx3 的图象都过点A(a，2)(1)求 A 点的坐标；(2)求该反比例函数的解析式分析：因为点A(a，2)在一次函数图象上，所以可将A 点坐标代入一次函数解析式，求得 A 点的坐标反比例函数解析式中只有一个待定系数，因此运用待定系数法只需一个点的坐标就可求函数解析式解：(1)将点 A(a，2)的坐标代入yx3 得 2a3，解得 a5，所以 A(5，2)(2)因为反比例函数ykx的图象过点A(5，2)，所以 2k5，解得 k10，所以 y10 x.设计意图：这一环节主要是复习待定系数法，再次应用这种重要的数学方法由已知条件确定反比例函数解析式，由于反比例函数解析式中只有一个待定系数，所以只需找到满足函数解析式的一个点的坐标即可活动四：基础练习教材第 3 页练习 1，2，3.备选练习：1张大叔预交了2 000 元手机话费，则这些话费能够使用的时间y(单位：月)与平均每月话费 x(单位：元)之间有怎样的函数关系？写出自变量的取值范围若平均每月用125 元，那么这些话费可以用多少时间？2已知 y 与 x2成反比例，且当x3 时，y4.(1)写出 y 关于 x 的函数解析式；(2)当 x1.5 时，求 y 的值3已知函数yy1y2，y1与 x2 成正比例，y2与 x 成反比例，且当x1 时，y0；当 x4 时，y9.当 x 1 时，求 y 的值文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 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ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3名师精编优秀教案(答案：1.y2 000 x(x0)，当 x125 时，y 16；2.(1)y36x2；(2)当 x 1.5 时，y16；3.当 x 1 时，y487.)活动五：课堂小结与作业布置课堂小结：1.什么是反比例函数，反比例函数的解析式有哪些形式？2如何根据已知条件求反比例函数的解析式？作业布置：教材第8 至 9 页第 1，2，4，6，7 题补充：1.当 m 取何值时，函数y2m2xm24 是 y 关于 x 的反比例函数？2已知函数yy1y2，y1与 x 成正比例，y2与 x 成反比例，且当x1 时，y4；当x2 时，y5.(1)写出 y 关于 x 的函数解析式；(2)当 x 2 时，求 y 的值(答案：1.m 2；2.(1)y2x2x；(2)当 x 2 时，y 5.)板书设计文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 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ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3名师精编优秀教案7C 学科网，最大最全的中小学教育资源网站，教学资料详细分类下载！文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 ZZ4K7N2Y4U3文档编码:CL5H10B8K2U6 HM6T4I9H8W5 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