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# Range (mathematics)

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

Given a function $f\colon A\rightarrow B$, 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:

$f\colon \mathbb{R}\rightarrow\mathbb{R}$

defined by

$f\colon\,x\mapsto x^2$

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,∞):

$0\leq f(x)<\infty.$