Function range

A function range in mathematics is a description of the possible values produced by a function.

Given a function f: A → 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: R → R

defined by

f: x → x²

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, ie the interval [0,∞):

0 ≤ f(x) < ∞

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See also: Function codomain, Function domain, Injective, Surjective, Bijective