Is the graph of $f(x) = (x^2-4)/(x-2)$ the same as $f(x) = (x+2)$? this might be a dumb question, but I was wondering what is the difference of graphs between $f(x) = (x^2-4)/(x-2)$  and $f(x) = (x+2)$. I understand if we simply the $f(x) = (x^2-4)/(x-2)$ it will come down to $f(x) = (x+2)$. But without simplifying it, they both behave differently at x = 2 and how would that impact their graph. I searched online, and all they would draw would be the same graph for both of them, but it doesn't feel right.

the graph of $f(x) = \frac{x^2-4}{x-2}$ is not defined at $x = 2$, it looks exactly like the graph of $x + 2$, but it has a hole at $f(2)$, graphic calculators usually don't graph that hole. Notice that $lim_{x\to\ 2} f(x)$ does exist, though $f(2)$ is not defined. when something like that happens, it is called a removable discontinuity, because we can define a new function $g(x) = f(x)$ if $ x \neq 2$ and $g(x) = 4$ if $x = 2$, this new function is continuous at 2. 
