Good! You are probably finding it difficult to show that function is not continous at 0 because it is continuous at 0!
Given any if x> 0, f(x)= x so we can just take . That way, "if , ". While if x< 0, f(x)= 0 so for any x and so for .
(The function is not differentiable at x= 0 but is continuous there.)