image

Image / Range

The image of a function $f:A\to B$ is the set of all output values it can produce:

$$\text{Im}(f):=\{f(a)\mid a\in A\}\subseteq B$$

It is a subset of the codomain $B$. Iff $f$ is surjective, then $\text{Im}(f)=B$.
Usually, the image of $A$ under $f$ is called the range of $f$, whereas $\{f(s)|s\in S\}\subseteq B$ is called the image of $S\subseteq A$ under $f$.