The modern notion of a function is derived from the efforts of many seventeenth- and eighteenth-century mathematicians. Of particular note was Leonhard Euler, to whom we are indebted for the function notation y = f(x). By the end of the eighteenth century, mathematicians and scientists had concluded that many real-world phenomena could be represented by mathematical models taken from a collection of functions called elementary functions.
Elementary functions fall into three categories.
- Algebraic functions (polynomial, radical, rational)
- Trigonometric functions (sine, cosine, tangent, and so on)
- Exponential and logarithmic functions
Source: Essential Calculus – Early Transcendental Functions by Ron Larson