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所谓函数的思想,就是运用运动和变化的观点,去分析和研究自然界中具体问题的各种数量间的依存关系,剔除问题中的非数学因素,抽象出蕴含在问题中的数学特征,用函数的形式把这种数量关系表示出来,建立起函数关系,加以研究,运用函数的知识(概念、图象和性质),使问题获得解决的思想.这种思想方法的精髓在于揭示问题中数量关系的本质特征,重在对于问题的变量的动态研究,从变量的运动变化、联系和发展的角度去寻找、打开和拓宽解决问题的思路.和函数思想有密切联系的就是方程思想.在解决问题时,用事先设定的未知数去沟通问题中所涉及的各种数量之间的制约关系,列出方程(组),从而求出未知数和各有关量的值,使
The so-called function of thinking, is the use of movement and change point of view, to analyze and study the nature of the specific problems in a variety of dependencies between the number of non-mathematical problems in the exclusion of the abstract out of the mathematical problems contained in the mathematical function, This quantitative relationship is expressed in terms of the relationship between the function, to study, use the knowledge of the function (concept, image and nature), to solve the problem of thinking.The essence of this method of thinking is to reveal the relationship between the number of problems , Focusing on the dynamic study of the variables of the problem, finding, opening up and broadening the way of solving the problem from the perspective of the change of the variables, the connection and the development.Effectiveness in solving the problem , The constraints between the various quantities involved in the problem are communicated using the previously set unknowns, the equations (groups) are listed, and the values of the unknowns and the relevant quantities are found