Based on the historical evolution and cognition′s development, this paper establishes a new definition of elementary functions, which is different from the traditional ones. Furthermore, it gives a simple criterion determining the elementarity of a piecewise function. Finally, it reviews the current related literatures and points out the problems which needs further investigation.%依据历史的延革、认知的进展，提出了关于初等函数的一个比较系统的概念；给出的限制域、存在域、定义域的概念，使函数的表达、相关的判断得以扩展，给出了分段函数初等性的一个简明的充分性判断；对于分段函数初等性主要的、广传的文献作了综述与评析，指出了存在的与需要研讨的问题。
展开▼
