1. ## Asymptotes

$f(x) = xe^{-x}$

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?

2. See this for example.

3. Originally Posted by tom ato
$f(x) = xe^{-x}$

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?
There is only one asymptote and that is a horizontal asymptote. You find it by considering the limit of the function as x --> +oo.

There is no vertical asymptote because there is no value of x for which the function is not defined.