25简单的幂函数(北师大版教案).pdf
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1、精品教学教案5 简单的幂函数教学目标：1了解指数是整数的幂函数的概念;2学会利用定义证明简单函数的奇偶性,了解用函数的奇偶性画函数图象和研究函数的方法；3培养学生从特殊归纳出一般的意识，培养学生利用图像研究函数奇偶性的能力。重点难点：1教学重点：幂函数的概念，奇偶函数的概念.2教学难点：幂函数图像性质，研究函数奇偶性。教学过程：一、情景引入(1)如果张红买了每千克1 元的蔬菜x千克,那么她需要支付yx(2)如果正方形的边长为x,那么正方形的面积2yx(3)如果立方体的边长为x,那么立方体的体积3yx(4)如果正方形的面积为x，那么正方形的边长yx(5)如果某人x秒内骑车行进 1 千米那么他骑车
2、的平均速度1yx以上问题中的函数有什么共同特征？yx2yx3yxyx12()yx1yx1()yx答：底数是自变量x,只是指数不同.二、知识探究学习资料总结-名师归纳欢迎下载-欢迎下载 名师归纳-第 1 页，共 4 页 -精品教学教案1、幂函数的定义：如果一个函数，底数是自变量x,指数是常量,即yx（是常数)，这样的函数叫幂函数.具体特点:底数是自变量指数是常量x的系数是 1 判一判：判断下列函数是否为幂函数.(1)myax2(2)yxx3nyx（）5(4)(2)yx2(5)2yx21(6)yx仅(3)是幂函数2、画出函数3yx的图像，讨论其图像特征（单调性、对称性等）解：列表：x2112012
3、12y811801818描点连线：图像特征:单调性:在 R 上是增加的对称性:函数图像 关于原点对称并且对任意 x,33fxxxfx即fxfx，像这样的函数叫作奇函数奇函数的特点：定义域关于原点对称对于定义域中的任意的x，都有fxfx、观察函数2fxx，讨论图像特征函数图像关于y轴对称，并且对任意x,22fxxxfxxyo1xyo1-1-1学习资料总结-名师归纳欢迎下载-欢迎下载 名师归纳-第 2 页，共 4 页 -文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2
4、J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V
5、9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I
6、9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:C
7、V2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV
8、6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH1
9、0I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码
10、:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1精品教学教案即fxfx，像这样的函数叫作偶函数偶函数的特点：定义域关于原点对称对于定义域中的任意的x，都有fxfx注：如果函数()yf x是奇函数或偶函数，我们就说函数()yfx具有奇偶性；根据奇偶性可将函数分为四类：奇函数、偶函数、既是奇函数又是偶函数、既不是奇函数也不是偶函数；注意：“任意”、“都有”等关键词，奇偶性是函数的整体性奇函数的图像关于原点对称，偶函数的图像关于y轴对称；奇、偶函数的定义域关于“0”对称如果一个函数的定义域不关
11、于“0”对称，则该函数既不是奇函数也不是偶函数；三、典型例题例 2 判断52fxx和4()2g xx的奇偶性.【课本 49 页动手实践】四、课堂训练1、画出下列函数的图像,判断其奇偶性.3(1)yx2(2)yx,x(3,3 2(3)yx32(4)y2(x1)12、判断函数()yf x在定义域R 上是奇函数,且在,0上是增加的的,则()f x在0,上也是增加的.(正确)函数()yf x在定义域R 上是偶函数,且在,0上是减少的,则()f x在0,上也是减少的.(错误)3、已知奇函数()fx,则()f ab,()fa=.已知偶函数()fx,则()f ab,()fa=.学习资料总结-名师归纳欢迎下载
12、-欢迎下载 名师归纳-第 3 页，共 4 页 -文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 ZH10I9H6F1O1文档编码:CV2J4R3B8A4 HV6V9B3U7X6 Z
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