Image

Definition

The image of a function is the set of all output values it may produce.

More generally, evaluating a given function $f$ at each element of a given subset $A$ of its domain produces a set, called the “image of $A$ under (or through) $f$”. Similarly, the inverse image (or preimage) of a given subset $B$ of the codomain of $f$, is the set of all elements of the domain that map to the members of $B$.

The above graphic shows a function $f$ from $X$ to $Y$. The blue oval $Y$ is the codomain of $f$. The red oval $X$ is the domain of $f$. The blue oval $Y$ is the codomain of $f$. The yellow oval inside $Y$ is the image of $f$.