A function $f$ is a rule that associates with each member $x$ of the set $A$ a unique member $y$ of the set $B$; we write

$\bullet$$A$ is called the domain of $f$, and

$\bullet$$B$ is called the codomain of $f$;

$\bullet$ the set of all values that are taken by $f$ is called the range of $f$; that is

When we write $f:A\rightarrow B$, we assume that $f(x)$ makes sense for all $x\in A$ and that $f(x)\in B$, so we take $B$ large enough to include all $f(x)$ and the codomain always includes the range.