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分式函数求最值(值域)问题深受命题者的青睐,频繁出现在各级各类竞赛试卷中.笔者对其作了长时间的整理之后,发现试题背后呈现出来的两种命制趋势:趋势1依据原型通过代换、变形打磨成试题;趋势2依据现有成题通过等价转化打磨成其他类型试题.笔者现以举例形式,尝试重现其构思设想过程如下,希望能给参加数学竞赛的师生提供有益的课程资源.
Fractional function to seek the most value (value) problem favored by the proponents, frequently appeared in all levels of competition papers.I made a long time after finishing it, I found the two kinds of life behind the test questions Trend: trend 1 based on the prototype by substitution, deformation grinding into test questions; trend 2 based on the existing problems into equivalent to other types of test questions. The author is now an example of the form, try to reproduce its conceptual design process is as follows, hoping to give Teachers and students participating in math competitions provide useful curriculum resources.