JEE Math Practice Question

$$f$$ is defined in $$\left[ { - 5,5} \right]$$ as $$f\left( x \right) = x$$ if $$x$$ is rational $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = - x$$ if $$x$$ is irrational. Then

1. A.$$f(x)$$ is continuous at every x, except $$x = 0$$
2. B.$$f(x)$$ is discontinuous at every $$x,$$ except $$x = 0$$
3. C.$$f(x)$$ is continuous everywhere
4. D.$$f(x)$$ is discontinuous everywhere