consider the simple function $f(x) = \left\{ \begin{array}{ll} 1 & \mbox{if $x \in [0,1]$}\\ 10 & \mbox{if $x \in \mathbb{Q} \cap [1,2]$}\\ -10 & \mbox{if $x \in \mathbb{Q^c} \cap [1,2]$}\\ 2 & \mbox{if $x \in [2,3]$}\ \end{array} \right.$
is it correct to say that f is continuous on $[0,1] \cup [2,3]$?