论文部分内容阅读
题目:已知正比例函数y=ax与反比例函数y=k/x的图象有一个交点A(1,2).(1)分别写出这两个函数的解析.(2)这两个函数的图象还有几个不同于点A的交点?请找出并说明理由.一、题目分析1.题目涉及的知识点与数学思想本题涉及正比例函数和反比例函数的图象与性质、待定系数法、交点的意义、反比例函数图象的对称性知识点等.涉及的数学思想有方程与函数的关系、转化思想(函数图象的交点转化为方程组的解),以及数形结合思想.
Title: It is known that there is an intersection point A (1, 2) for the image with the positive proportional function y = ax and the inverse proportional function y = k / x. (1) Analyze the two functions separately. (2) Image There are several points different from the intersection of point A Please find out and explain the reason I. Topic Analysis 1. Subjects involved in the knowledge and mathematical thought This question relates to the image and the nature of the proportional function and inverse function of the coefficient to be determined Law, the meaning of the intersection point, the symmetry knowledge point of the inverse proportion function image, etc. The mathematical ideas involved are the relationship between the equation and the function, the transformation idea (the intersection of the function image is transformed into the solution of the system of equations), and the idea of number-shape combination.