Graph of $\quad\frac{x^3-8}{x^2-4}$. I was using google graphs to find the graph of $$\frac{x^3-8}{x^2-4}$$ and it gave me:

Why is $x=2$ defined as $3$? I know that it is supposed to tend to 3. But where is the asymptote???

There will only be an asymptote if the limit is infinity. in your case, for all points $x\neq 2$:
$$\frac{x^3-8}{x^2-4} = \frac{x^2+2x+4}{x+2} $$
Which has no discontinuities! 
