Function (nonfiction)

A function f takes an input x, and returns a single output f(x). One metaphor describes the function as a "machine" or "black box" that for each input returns a corresponding output.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

An example is the function that relates each real number x to its square x2.

The output of a function f corresponding to an input x is denoted by f(x) (read "f of x").

In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9.

Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9. (The same output may be produced by more than one input, but each input gives only one output.)