Define a function $f\left(x\right)=\{\begin{array}{c}\sin x,ifxisirrational\\ \tan x,ifxisrational\end{array}.$ Then f (x) is

not continuous at any point in the interval $(-\pi ,\pi )$

continuous at some point(s), but not differentiable at any point in the interval $(-\pi ,\pi )$

continuous at some point(s) in the interval $(-\pi ,\pi ),$ but not differentiable at some of these point(s)

continuous at some point(s) in the interval $(-\pi ,\pi )$ and differentiable at all these point(s)