If I have the piecewise function:

$f(x) = x+2$ when $x \in [0,1]$ and $x-2$ when $x \in [2,3]$ being mapped from $[0,1]\cup[2,3]$ to $[0,1]\cup[2,3]$

how do I show that the function is continuous? I do know how to show continuity when there is a break in intervals of the functions. I think I need to show one sided limits but I do not know where to start. I am pretty confused.