elementary set theory - Examples of surjective functions $mathbb{Nto Z}$ and $mathbb{Nto Ntimes N}$

I'm asked to give examples of surjective functions $\mathbb{N} \rightarrow \mathbb{Z}$ and $\mathbb{N} \rightarrow \mathbb{N} \times \mathbb{N}$. Could a function $\mathbb{N} \rightarrow \mathbb{Z}$, just be $\mbox{floor}(x)$, and a function $\mathbb{N} \rightarrow \mathbb{N} \times \mathbb{N}$ be $x^2$? In both cases, every element in the codomain would be mapped to. Or is it meant to be a function like: $x \mapsto (x,y)$?