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构建函数模型是历年的常考题型,正如法国著名数学家笛卡儿所说:“我们所解决的每一个问题,将成为一个模式,以用于解决其他问题”.通过模型进而利用一次函数或反比例函数或二次函数、方程(组)、不等式、三角函数等知识设计不同的方案,或制定一个最佳方案解决实际问题.它既符合素质教育提出的“培养学生应用意识”的新要求,同时也有利于培养学生分析问题和解决问题的能力,解这类数学应用题的关键是通过对问题原始形态的分析、联想和抽象,将实际问题转化为一个数学问题,即构建一个函数数学模型.下面举例分析说明.
Constructing a function model is a constant test type over the years, as the famous French mathematician Descartes put it: “Every problem we solve will be a model that will be used to solve other problems.” By using the model one more time Function or inverse function or quadratic function, equation (group), inequality, trigonometric function, etc., or to design a best solution to solve practical problems.It is not only in line with the “quality of students’ awareness of application” , But also conducive to students’ ability to analyze and solve problems. The key to solving such math problems is to transform the actual problem into a mathematical problem through the analysis, association and abstraction of the original form of the problem, that is, to construct A mathematical model of function.