[高一数学必修一_函数的奇偶性_课件.ppt

课前热身 1 1 2.函数f(x)=2x2-mx+3，当x∈(-∞,-1]时是减函数，当x∈(-1,+∞)时是增函数，则f(2)= _______. 19 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 利用函数的单调性求函数的最值 3、求函数f(x)＝x＋ 的最大值和最小值． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. x y o 1 2 3 4 5 -1 1 2 3 -1 -2 -3 观察下图，思考并讨论以下问题： （1）这两个函数图象有什么共同特征吗？ （2）相应的两个函数值对应表是如何体现这些特征的？ 一、引入新课 x y o 1 2 3 -1 1 2 -1 3 x f(x)=|x| … … -3 3 -2 2 -1 1 0 0 1 1 2 2 3 3 … … x f(x)=x2 … … -3 9 -2 4 -1 1 0 0 1 1 2 4 3 9 … … 这两个点的坐标 有什么关系? (x,f(x)) (-x,f(-x)) ● ● 函数的图象关于y轴对称 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 当自变量任取两个互为相反数的值时， 对应的函数值相等。 x f(x)=x2 … … -3 9 -2 4 -1 1 0 0 1 1 2 4 3 9 … … Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二、新课讲解 一般地,如果对于函数f(x)的定义域内任意一个x,都有f(-x)=f(x), 那么函数f(x) 就叫做偶函数. 思考:定义中“任意一个x,都有f(-x)=f(x)成立”说明了什么？ 说明f(-x)与f(x)都有意义， 即-x、x必须同时属于定义域， 因此偶函数的定义域关于原点对称。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Clien