Range of a function - Definition and Overview

In mathematics, the range of a function is the set of all values produced by a function. Sometimes called the image.

Given a function <math>f\colon A\rightarrow B<math>, the set f(A) is called the range of f. The range is not to be confused with the codomain B. Generally the range is only a subset of the codomain.

Example

Let the function f be a function on the real numbers:

<math>f\colon \mathbb{R}\rightarrow\mathbb{R}<math>

defined by

<math>f\colon\,x\mapsto x^2<math>

The codomain of f is R, but clearly f(x) never takes negative values, and thus the range is in fact the set R⁺—non-negative reals, i.e. the interval [0,∞):

<math>0\leq f(x)<\infty.<math>

See also

codomain, domain (mathematics), injective function, surjective function, bijective function