Codomain

Definition

The codomain of a function is the set into which all of the output of the function is constrained to fall. It is the set $Y$ in the notation $f:X \rightarrow Y$. The term range is sometimes ambiguously used to refer to either the codomain or image of a function.

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 $f$.