What kind of function is represented by this graph?

Question

What kind of function is represented by this graph?

I've created an example for this question:

For every $x$ I increase $y$ by $1$. But for every fourth $x$-value I increase $y$ by $2$ instead of $1$. I wonder how I could describe this by a function.

Answer 1

$y(x) = x + \lfloor x/4 \rfloor$ for $x \in \mathbb{Z}$.

Answer 2

It is a piecewise function.

$$1\le x\le 3 \implies f (x)=x $$

$$4\le x\le 7 \implies f (x)=x+1$$ $$f (8)=10$$