Unary function is partially n-computable
Well there are trivial two conditions you have to prove.
If $f:N\rightarrow N$ is computable in $n$ instructions, then there exists a corresponding program $P$ that computes it in $n$ instructions. $P$ could assign one new variable in every instruction, thus the program uses $\leq n$ new variables. Furthermore the program only contains $n$ instructions meaning there is one label for every instruction at max, hence the number of labels is $\leq n$. This completes the proof (that $f$ is partially n-computable)