Let
$f(x) = \begin{cases}\;\;\, x\;\;,\;\text{ if } x \in \mathbb{Q}\\ -x\;\;,\; \text{ if } x \in \mathbb{R}\setminus \mathbb{Q} \end{cases}$
(i) Determine the point or points of continuity of $f$. (ii) Show that the point of points of continuity of $f$ are the only points.
Clearly its continuous at $0$. I'm not sure how to prove it is continuous at $0$, but I know how to prove that it has no other points of continuity.