高一数学函数的奇偶性_人教版2.ppt

函数的奇偶性 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. 对称现象 蝴蝶 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. 雪花晶体 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. 引 例： 1.已知函数f(x)=x2,求f(-2),f(2), f(-1),f(1),及f(-x) ,并画出它的图象。 解: f(-2)=(-2)2=4 f(2)=4 f(-1)=(-1)2=1 f(1)=1 f(-x)=(-x)2=x2 2.已知f(x)=x3,画出它的图象,并求出f(-2),f(2),f(-1),f(1)及f(-x) 解: f(-2)=(-2)3=-8 f (2)=8 f(-1)=(-1)3=-1 f(1)=1 f(-x)=(-x)3=-x3 思考 : 通过练习,同学们发现了什么规律? f(-2)=f(2) f(-1)=f(1) f(-x)=f(x) f(-2)= - f(2) f(-1)= - f(1) f(-x)= - f(x) -x x f(-x) f(x) -x f(-x) x f(x) 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. 1.函数奇偶性的概念: 偶函数定义: 如果对于f(x)定义域内的任意一个x, 都有f(-x)=f(x), 那么函数f(x)就叫偶函数. 奇函数定义: 如果对于f(x)定义域内的任意一个x, 都有 f(-x)=-f(x),那么函数f(x)就叫奇函数. 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. 对奇函数、偶函数定义的说明: (1). 定义域关于原点对称是函数具有奇偶性的必要条件。 （2）.奇、偶函数定义的逆命题也成立，即： 若f(x)为奇函数, 则f(-x)=－f(x)成立。 若f(x)为偶函数, 则f(-x)= f(x) 成立。 （3） 如果一个函数f(x)是奇函数或偶函数,那么我们就说函数f(x) 具有奇偶性。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Cop