Answer
See sample answer below.
Work Step by Step
$f(x)\left\{\begin{array}{lll}
1, & if & x\not\in\{0,1,2\}\\
0 & if & x\in\{0,1,2\}
\end{array}\right.$
is defined everywhere. It is continuous everywhere except at $x=0$, $x=1$, and at $x=2$.