开放型问题是相对于有明确条件和明确结论的封闭型问题而言的,这类试题的知识覆盖面较大综合性较强,灵活选择方法的要求较高,再加上题意新颖,构思精巧,具有一定的深度和难度,这种题重在考查学生的分析、探索能力和思维发散能力,下面,笔者对函数中的开放型问题进行分类解析,以供同行参考.一、函数单调性开放型问题例1设函数f(x)=(X~2+1)~(1/2)其中a>0,求a的取值范围,使函数f(x)在[0,+∞)上是单调函数. Open-ended questions are relative to closed-ended questions that have definite conditions and clear conclusions. The coverage of such questions is relatively comprehensive and comprehensive, and the requirements of flexible choice methods are high. In addition, the questions are novel and sophisticated , With a certain degree of depth and difficulty, this emphasis on examining students’ ability to explore and disseminate the ability of thinking, the following, the author of the open-type function in the classification analysis for peer reference. (1) Let the function f (x) be on [0, + ∞), where a> 0, find the range of a Is a monotonous function.