For what values is $f$ continuous?

$$f(x) = \begin{cases} 0 & \textrm{if }x\textrm{ is rational}\\ x & \textrm{if }x\textrm{ is irrational} \end{cases}$$

(a) $x=0$
(b) All rational $x$.
(c) All irrational $x$.
(d) All $x$.
(e) For no $x$.