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函数是中学数学的重点内容,研究函数的单调性则是函数问题的一个主要课题。把分散在教材各个部分的面广量大的讨论函数单调性的命题和结论巧妙地归纳起来,从中提炼出更具有代表性的基本结论,这是帮助学生加深对函数单调性的理解,增强解题能力的重要途径。本文以“奇、偶函数的单调性”的讨论为例,谈谈我在归纳、提炼过程中的做法。我们约定,如果函数y=f(x) 在所讨论的两个区间M_1和M_2上都是递增(减)的,则称函数在这两个区间上有同向单调性;反之,则称函数在这两个区间上有异向单调性。由此,可得到如下两个很有实用价值的基本结论。结论1.若函数y=f(x)为奇函数,则它在定义域内关于原点对称的两个区间M_1和
The function is the key content of the middle school mathematics. Studying the monotonicity of the function is a major issue of the function problem. Summarize the propositions and conclusions about the monotonous nature of the discussion function, which is scattered in all parts of the textbook, and extract the more representative basic conclusions from it. This is to help students to deepen their understanding of the monotonicity of function and enhance the solution An important way to ask questions. This article takes the discussion of “the monotony of even and odd functions” as an example to talk about my practice in induction and extraction. We agree that if the function y = f (x) is incremented (subtracted) over both of the two intervals M_1 and M_2 in question, then the function is said to have a monotonicity in both of these intervals; conversely, the function In these two intervals are monotonous. Thus, we can get the following two basic conclusions of great practical value. Conclusions 1. If the function y = f (x) is an odd function, then it defines two intervals M_1 and