You Gotta Know These Classifications of Mathematical Functions

A function in mathematics is an association between input values and output values, in which each input value is associated with exactly one output value. That association is often given by a formula, and it is that sort of function that this article will focus on. However, a function could be defined in other ways, such as by a table (as one might make for scientific observations) or simply by a description (for instance, your distance from home is a function of the time of day, since at each time of day you are at exactly one place, and therefore a particular distance from home).

The set of possible input values for a function is called its domain, and the set of possible output values is called the codomain. The term “range” is sometimes used instead of “codomain,” but “range” is also sometimes used to mean “image” (see below), so “range” is confusing and NAQT generally avoids it. The domain and codomain of a function could be any set at all — consisting of numbers, matrices, people, flowers, etc. — but most of high school and earlier math, and this article, are concerned with functions whose domain and codomain are both sets of numbers (especially the set of all real numbers).

Mathematical functions can be classified based on properties of formulas, how the functions can be used, features of their graphs, and in other ways. As a result of these multiple classifications, many functions are in more than one of the following categories.

This article was contributed by NAQT member Jonah Greenthal.

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