Expert: Ahmed Salami - 4/20/2009

Question
what does it mean when they say that a functions graph approaches infinity as it gets closer to a vertical asymptote?

Answer
Hi Kami,
The line x = k is a vertical asymptote of a curve y = f(x) if the limit of f(x) as x approaches k is infinity.
What your statement means is that the value of the function keeps on increasing without bound as the independent variable approaches the value at which the asymptote occurs. Typically, the vertical asymptote is a vertical line that the function graph gets closer and closer to but never actually touches.
Theoretically, we say that a function intersects its asymptote at infinity, try to imagine that.

Regards