论文部分内容阅读
运用运动和变化的观点分析和研究具体问题的数量关系,通过函数的形式,把这种关系表示出来并加以研究,从而使问题获得解决,这种思想方法,叫做函数思想法。纵观近几年的高考试题,笔者发现有许多命题与函数思想法有着较为密切的联系。下面举例说明。 例1 已知(1-2x)~7=a_0+a_1x+…a_7x~7,那么a_1+a_2+…+a_7= (1989年试题) 解:没函数f(x)=(1-2x)~7,则f(x)=a_0+a_1x+…+a_7x~7,又f(1)=a_0+a_1+a_2+…+a_7=-1,f(0)=a_0=1, ∴a_1+a_2+…a_7=f(1)-f(0)=-2. 例2 解不等式.(1985年试题) 解:设函数,则此函数的定
The use of movement and change perspectives to analyze and study the quantitative relationship of specific problems, through the form of functions, to express and study the relationship, so as to make the problem to be resolved, this method of thinking, called the function of thought. Looking at the high exam questions in recent years, the author found that there are many propositions that have a close connection with the functional thinking method. The following is an example. Example 1 Known (1-2x)~7=a_0+a_1x+...a_7x~7, then a_1+a_2+...+a_7= (1989 test) Solution: No function f(x)=(1-2x)~7, Then f(x)=a_0+a_1x+...+a_7x~7, and f(1)=a_0+a_1+a_2+...+a_7=-1,f(0)=a_0=1, ∴a_1+a_2+...a_7=f (1) -f(0) = -2. Example 2 Solution of inequality. (Question 1985) Solution: Set function, then set the function