Answer
See graph
Work Step by Step
We are given the function:
$f(x)=\begin{cases}
\dfrac{x^2-x-2}{x-2},\text{ if }x\not=2\\
4,\text{ if }x=2
\end{cases}$
Rewrite the function:
$f(x)=\begin{cases}
\dfrac{(x-2)(x+1)}{x-2},\text{ if }x\not=2\\
4,\text{ if }x=2
\end{cases}$
We can simplify the fraction as $x\not=2$:
$f(x)=\begin{cases}
x+1,\text{ if }x\not=2\\
4,\text{ if }x=2
\end{cases}$
We graph $y=x+1$ for $x\in(-\infty,2)\cup(2,\infty)$ and the point $(2,4)$ corresponding to $x=2$:
