LiMit of Vertical FUNCTION question?

Question

If a graph has a vertical asymptote and the limit of the function is infinity or negative infinity on BOTH SIDES of the asymptote is there a way to know this just by the actual function. I know there's a way to differentiate this kind of graph from a graph that has one side going to infinity and another to negative infinity, I just don't know how. Thank you.

Answer 1

Yes. If your function is a fraction (basically), denominator has a variable, and if the whole denominator can go to zero, it will have the vertical asymptote that either go positive infinity, negative infinity , or both. You will have to analize the limit as it approach the zero from left and the right to determine which is the case.