Surjective function

A function $f:A\to B$ is called onto or a surjective function if every element $b$ in $B$ can be obtained as $b = f(a)$ for some $a$ in $A$. To summarise, the entire codomain must be mapped to the domain.

Example of a Surjective mapping

In general, this might not be the case. If $f$ is an $A\to B$ function, we know that for every $a\in A$, we have $f(a)\in B$. If the range of $f$ can be a proper subset of $B$ (which is the codomain), then it is not onto.