Range

Let $A$ and $B$ be any sets and let $f:A\to B$ be any function between them, so that $A$ is the domain of $f$ and $B$ is the codomain. Then $\{b\in B\mid \mathrm{there\ is\ some\ } a\in A\mathrm{\ such\ that\ } f(a)=b\}$ is called the range or image of $f$.

Thus, if we have $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = x^2$, the range of $f$ is the set of nonnegative real numbers.

A function is a surjection exactly when the range is equal to the codomain.

See also

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