文档介绍：对数函数及其性质对数函数及其性质( (一一) ) 第二章基本初等函数( Ⅰ) Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 值域: (0,+ ∞) Ox y1 1y=a x(a>1) y=a x (0<a<1) Ox y1 1 定义域: R过点(0,1), 即当 x=0时, y=1 在R上是增函数; 在R上是减函数. 函数性质 a>1 0<a<1 :既不是奇函数也不是偶函数 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 二、引入新知 :一般地我们把函数)1,0( log???aaxy a且叫做对数函数,其中 x是自变量,定义域为。?(0,+ ) 思考:通过对数函数定义的研究,我们对定义中应该注意的问题有哪些呢? 用描点法画出图象 2 log y x ?? ? xy 2 1 log ? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 为例,用描点法画图. 分别以 2 log y x ?? ? xy 2 1 log ?和 yx 0 1 -2 3 -3 21348765 2 -1 xy 2 log ?xy 2 1 log ? 12468 -1 012 3 10 -1 -2 - -3 2 log y x ? 12 log y x ?x12 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 1 (a>1)(0<a<1) 对数函数的图象有 2种情况· · yx O log a y x ?1 性质定义域值域定点单调性( 0 , + ∞)R ( 1 , 0 ) 当 a>1 时,在( 0 , + ∞ ) 上是增函数当 0<a<1 时,在( 0 , + ∞) 上是减函数 : Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. : xy 2 log ?xy 2 1 log ?在同一直角坐标系中分别画出,及,的图象,观察其特点。 xy 3 log ?xy 3 1 log ?x yO xy 2 log ?xy 3 log ?xy 3 1 log ?xy 2 1 log ? 2 13 1大按顺时针方向a由小