EJMT Abstract

What is a transcendental function? Whether they realize it or not, most students are quite familiar with these functions. In this paper, we first seek to unravel and explain the terms ”algebraic” and ”transcendental” in the context of numbers and then in the context of functions. We then prove some basic results establishing that exponential, logarithmic, trigonometric, and inverse trigonometric functions are transcendental. We also briefly discuss the nature of an “elementary function.” The paper concludes with a series of reader investigations exploring these concepts in a computer algebra system such as Maple.