The problem I am looking at is $\displaystyle f(x) = \frac{x - 3}{x^2 - 9}$

I found that f was not defined at $\displaystyle x = \pm 3$

I have -3 as a non-removable discontinuity, and 3 as a removable discontinuity, approaching positive infinity from either side. Yet, when I graph the function, it is unequivocally approaching a finite value. Why did limiting process give me positive infinity?