I have this piecewise function:
f(x)=\begin{cases}
\dfrac{x^2-x-2}{|x-2|}, & x \neq 2 \\
0, & x = 2\text{.}
\end{cases}
I can't figure out how to graph it. I punched these numbers into my calculator, and it created a parabola, but I haven't been able to get there on my own without the calculator.
So far I have plotted the point (2,0) on my graph, and I factored the first function to
\dfrac{(x-2)(x+1)}{|x-2|}
and now I am stuck. I tried multiplying both the top and bottom by x+2, but after simplifying I ended up with x+1, which I am pretty positive is not correct.
Where did I go wrong?
