Looking at the equation, the Domain of the function should be all reals, but when I graph it on my calculator, there appears to be a horizontal asymptote right above zero and a vertical asymptote somewhere in the 3rd quadrant (the function suggests that y should continue to grow smaller (more negative) on into infinity, but it's like the paradox of in order to move from a to b, you must first move half way there, and half way to half way, and so on).

How do I find the asymptotes algebraically?