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《普通高中数学新课程标准》(实验)倡导积极主动、勇于探索的学习方式,使学生学会自主学习,为终身学习和终身发展打下良好的基础,这些是高中数学课程追求的基本理念之一.本文就学生提出“把反比例函数y=k/x(k≠0)的图像叫双曲线是科学的吗”的疑问,利用学生已有的知识,采用合情逆推的方式指导学生探索,得出反比例函数y=k/x(k≠0)的图像就是双曲线,并得到双曲线y=k/x(k≠0)的一些性质.
The “New High School Mathematics Curriculum Standard” (experiment) advocates proactive and courageous exploration, which enables students to learn independently and lay a good foundation for lifelong learning and lifelong development. These are one of the basic concepts pursued by high school mathematics curriculum. In this paper, the students put forward the question “Is the hyperbola scientifically the image of inverse proportion function y = k / x (k ≠ 0)”, using the existing knowledge of students to guide students to explore , The image that yields the inverse function y = k / x (k ≠ 0) is a hyperbola, and some properties of the hyperbolic y = k / x (k ≠ 0) are obtained.