I've not really understood why this happens. I'm quite new to the idea of limits, etc. But I've seen that when you use a grapher, it plots undefined points. For example in the function $f(x) = \frac{x^2+x-6}{x-2}$, the value $f(2)$ would be undefined, so why does a grapher not show that $f$ is undefined at $2$ and instead carries on through it? It seems to be plotting the $\lim\limits\_{x \to 2} \frac{x^2+x-6}{x-2}$.

I hope this makes sense, apologies if it doesn't. 

![Graph of $\frac{x^2+x-6}{x-2}$](https://i.stack.imgur.com/EtWD1.png)