Range of a function

Definition

Let $f \colon A \to B$ be a function. The range of $f$ is the set $$\operatorname{ran}(f) = \{f(a) \mid a \in A\} = \{b \in B \mid \exists a \in A, \, f(a) = b\}.$$

Remarks

The range is also called the image of $f$, and it is the image $f(A)$ of the whole domain. Some authors use "range" for the codomain. This node uses the meaning above. For $f \colon \mathbb{R} \to \mathbb{R}$ with $f(x) = x^2$, the range is $[0, \infty)$.

Explanations

L1 human

The range is the set of outputs that actually occur. It can be smaller than the codomain.