Question

Can somone explain when the horizontal asymptotes can be crossed? I looked online, and the explanations are just confusing. Please help.

Answer 1

Difficult question to answer here. Involves the calculus.

Answer 2

yes, they can be crossed
i can give two easy examples

Answer 3

The question is WHEN can they be crossed. That is a complicated question to answer here.

Answer 4

\[\frac{1}{x^2-1}\] as a horizontal asymptote at \(y=0\) but it crosses the \(x\) axis

Answer 5

Well, I am working on a graph involving asymptotes right now, and the horizontal asymptote is apparently crossed (When I graphed it it showed) However, I am confused on how to algebraically see whether the horizontal asymptote is crossed or not.

Answer 6

@satellite73 Can you explain why please?

Answer 7

ok i lied, my example was wrong
here is a better one
\[y=\frac{x}{x^2-1}\]

Answer 8

that has a horizontal asymptote at \(y=0\) aka the \(x\) axis

Answer 9

but it clearly crosses the \(x\) axis because if \(x=0\) you get \(y=0\)

Answer 10

horizontal asymptote is what the function does as \(x\to \infty\) or \(x\to -\infty\)
what it does in the middle is not relevant so it can cross it

Answer 11

Oh ok, so as long as it is in the middle, it can cross the Horizontal asymptote (under specific circumstances)?

Answer 12

yes it can cross it
in fact, although you have probably not seen these, it can cross infinitely often

Answer 13

Ok thank you. That cleared up some misunderstandings I had.

Answer 14

here is an example
\[y=\frac{\sin(x)}{x}\]
http://www.wolframalpha.com/input/?i=sin%28x%29%2Fx

Answer 15

the vertical asymptote cannot be crossed