本文是清华大学李欧先生在北京市海淀区教师进修学校组织的报告会上所作的演讲的讲演稿。文章以历史发展为线索,揭示了函数概念是如何逐步精确化的。文章深入浅出地论述了各种函数定义的实质,并对教师们在教学中遇到的一些主要问题作了解答。本文对教师进修和教学都有重要参考价值。本刊征得李先生同意发表如下。 This article is a speech delivered by Mr. Li Ou of Tsinghua University at a report organized by the Teacher Training School of Haidian District, Beijing. Taking the historical development as a clue, the article reveals how the concept of functions is gradually refined. The article discusses the essence of various function definitions in a simple and easy-to-understand manner and answers some of the major problems encountered by teachers in teaching. This article has important reference value for teachers’ education and teaching. The publication seeks Mr. Li’s agreement to be published as follows.