2022年人教A版数学必修一2.2.1《幂函数》教案 .pdf

名师精编优秀教案2.2.1幂函数（两课时）教学目标：知识与技能通过具体实例了解幂函数的图象和性质，并能进行简单的应用过程与方法能够类比研究一般函数、指数函数、对数函数的过程与方法，来研究幂函数的图象和性质情感、态度、价值观体会幂函数的变化规律及蕴含其中的对称性教学重点：重点从五个具体幂函数中认识幂函数的一些性质难点画五个具体幂函数的图象并由图象概括其性质，体会图象的变化规律教学程序与环节设计：创设情境组织探究尝试练习巩固反思作业回馈课外活动问题引入幂函数的图象和性质幂函数性质的初步应用复述幂函数的图象规律及性质幂函数性质的初步应用利用图形计算器或计算机探索一般幂函数的图象规律名师精编优秀教案教学过程与操作设计：环节教学内容设计师生双边互动创设情境阅读教材P90的具体实例（1）（5），思考下列问题：1它们的对应法则分别是什么？2以上问题中的函数有什么共同特征？（答案）1（1）乘以 1；（2）求平方；（3）求立方；（4）开方；（5）取倒数（或求1 次方）2上述问题中涉及到的函数，都是形如xy的函数，其中x是自变量，是常数生：独立思考完成引例师：引导学生分析归纳概括得出结论师生：共同辨析这种新函数与指数函数的异同组织探究材料一：幂函数定义及其图象一般地，形如xy)(Ra的函数称为幂函数，其中为常数下面我们举例学习这类函数的一些性质作出下列函数的图象：（1）xy；（2）21xy；（3）2xy；（4）1xy；（5）3xy 解 1列表（略）2图象师：说明：幂函数的定义来自于实践，它同指数函数、对数函数一样，也是基本初等函数，同样也是一种“形式定义”的函数，引导学生注意辨析生：利用所学知识和方法尝试作出五个具体幂函数的图象，观察所图象，体会幂函数的变化规律师：引导学生应用画函数的性质画图象，如：定义域、奇偶性师生共同分析，强调画图象易犯的错误环节教学内容设计师生双边互动文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 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ZT4E9Q5Z10N4名师精编优秀教案组织探究材料二：幂函数性质归纳（1）所有的幂函数在（0，+）都有定义，并且图象都过点（1，1）；（2）0时，幂函数的图象通过原点，并且在区间),0上是增函数特别地，当1时，幂函数的图象下凸；当10时，幂函数的图象上凸；（3）0时，幂函数的图象在区间),0(上是减函数在第一象限内，当x从右边趋向原点时，图象在y轴右方无限地逼近y轴正半轴，当x趋于时，图象在x轴上方无限地逼近x轴正半轴师：引导学生观察图象，归纳概括幂函数的的性质及图象变化规律生：观察图象，分组讨论，探究幂函数的性质和图象的变化规律，并展示各自的结论进行交流评析，并填表材料三：观察与思考观察图象，总结填写下表：xy2xy3xy21xy1xy定义域值域奇偶性单调性定点材料五：例题 例 1（教材 P92例题）例 2 比较下列两个代数值的大小：（1）5.1)1(a，5.1a（2）322)2(a，322 例 3 讨论函数32xy的定义域、奇偶性，作出它的图象，并根据图象说明函数的单调性师：引导学生回顾讨论函数性质的方法，规范解题格式与步骤并 指 出 函 数 单调性是判别大小的重要工具，幂函数的图象可以在单调性、奇偶性基础上较快描出生：独立思考，给出解答，共同讨论、评析环节呈现教学材料师生互动设计文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 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ZT4E9Q5Z10N4名师精编优秀教案2已知幂函数)(xfy的图象过点)2,2(，试求出这个函数的解析式3在固定压力差（压力差为常数）下，当气体通过圆形管道时，其流量速率R与管道半径r 的四次方成正比（1）写出函数解析式；（2）若气体在半径为3cm的管道中，流量速率为 400cm3/s，求该气体通过半径为r 的管道时，其流量速率R的表达式；（3）已知（2）中的气体通过的管道半径为5cm，计算该气体的流量速率41992 年底世界人口达到548 亿，若人口的平均增长率为x%，20XX年底世界人口数为y（亿），写出：（1）1993 年底、1994 年底、2000 年底的世界人口数；（2）20XX年底的世界人口数y 与 x 的函数解析式课外活动利用图形计算器探索一般幂函数xy的图象随的变化规律收获与体会1 谈谈五个基本幂函数的定义域与对应幂函数的奇偶性、单调性之间的关系？2 幂函数与指数函数的不同点主要表现在哪些方面？文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 ZT4E9Q5Z10N4文档编码:CY1O5D3Y5F8 HI6T7G2R5I1 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