# $f$ is defined in [-5,5] as $f(x)=\left\{\begin{array}{1 1}x&if\;x\;is\;rational\\-x&if\;x\;is\;irrational\end{array}\right.$. Then
$\begin{array}{1 1}(A)\;\text{f(x) is continuous at every x,except x=0}\\(B)\;\text{f(x) is discontinuous at every x,except x=0}\\(C)\;\text{f(x) is continuous everywhere}\\(D)\;\text{f(x) is discontinuous everywhere}\end{array}$