# Range of a function

## Subset of a function's codomain / From Wikipedia, the free encyclopedia

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In mathematics, the **range of a function** may refer to either of two closely related concepts:

Given two sets X and Y, a binary relation f between X and Y is a (total) function (from X to Y) if for every x in X there is exactly one y in Y such that f relates x to y. The sets X and Y are called domain and codomain of f, respectively. The image of f is then the subset of Y consisting of only those elements y of Y such that there is at least one x in X with *f*(*x*) = *y*.