It's a cycloid.

The parametric equations that describe it are $$x = r(\theta-\sin\theta), \quad y=-r(1-\cos\theta)$$ where $\theta$ is a parameter, and the curve is traced out from the origin.

If you substitute the $y$ equation into the $x$, you can get a relation of the form

$$x=\arccos\bigg( 1+\dfrac yr\bigg)-\dfrac{\sqrt{r^2-(r+y)^2}}r$$

which is as "close" as you can get to a an "exact function," though note that the above relation is restricted for $0\leq x\leq \pi$.

It's a cycloid.

The parametric equations that describe it are $$x = r(\theta-\sin\theta), \quad y=-r(1-\cos\theta)$$ where $\theta$ is a parameter, and the curve is traced out from the origin.

If you substitute the $y$ equation into the $x$, you can get a relation of the form

$$x=\arccos\bigg( 1+\dfrac yr\bigg)-\dfrac{\sqrt{r^2-(r+y)^2}}r$$

which is as close as you can get to a an "exact function," though note that the above relation is restricted for $0\leq x\leq \pi$.