高一数学函数单调性.ppt

文档介绍：3 2 1 , x y x y x ???问题分别作出函数y=2以及的图象,并且观察当自变量变化时,函数值有什么变化规律? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. x yo )(xfy?mn x yo )(xfy?mn [m,n]上,函数 y随x的增大而减小在[m,n]上,函数 y 随x的增大而增大——单调递增性——单调递减性通俗定义问题 2 能否根据自己的理解说说什么是增函数、减函数? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. )x(fy?Ox y)x(f 11x )x(f 22x如何用 x与 f(x) 来描述上升的图象? 函数 f (x) 在给定区间上为增函数。这个给定的区间就为单调增区间。) f(x ) f(x 2 1? 21xx?在给定的区间上任取 x 1, x 2; Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. )x(fy?y)x(f 1)x(f 2Ox 1x 2x如何用 x与 f(x) 来描述下降的图象? 函数 f (x) 在给定区间上为减函数。这个给定的区间就为单调减区间。) f(x ) f(x 21? 21xx?在给定的区间上任取x 1,x 2; Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. -5 Ox y12345 -1 -2 -3 -4 1 2 3 -1 -2 例 1 下图是定义在[-5, 5]上的函数 y=f(x) 的图象,根据图象说出 y=f(x)的单调区间,以及在每一单调区间上, y=f(x)是增函数还是减函数? 解: y=f(x)的单调区间有[-5,- 2), [-2,1) [1,3), [3, 5]. 其中 y=f(x)在[-5,- 2), [1,3)上是减函数, 在[-2,1), [3 ,5). Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. yx o y=kx+b ( k>0 ) yx o y=kx+b ( k<0 ) 讨论一次函数的单调性问题: 1、当 k变化时函数的单调性有何变化? 2、当 b变化时函数的单调性有何变化? end 返回结论: 上为增函数) , 时,在( ?????0a 上为减函数)