Editing Range of a function (section)

{{Short description|Subset of a function's codomain}}
{{For|the statistical concept|Range (statistics)}}[[Image:Codomain2.SVG|right|thumb|350px|<math>f</math> is a function from [[domain of a function|domain]] '''''X''''' to [[codomain]] '''''Y'''''. The yellow oval inside '''''Y''''' is the [[Image (mathematics)|image]] of <math>f</math>.  Sometimes "range" refers to the image and sometimes to the codomain.]]

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

* the [[codomain]] of the [[function (mathematics)|function]], or
* the [[image (mathematics)|image]] of the function.

In some cases the codomain and the image of a function are the same set; such a function is called ''[[surjective function|surjective]]'' or ''onto''. For any non-surjective function <math>f: X \to Y,</math> the codomain <math>Y</math> and the image <math>\tilde Y</math> are different; however, a new function can be defined with the original function's image as its codomain, <math>\tilde{f}: X \to \tilde{Y}</math> where <math>\tilde{f}(x) = f(x).</math> This new function is surjective.