Are there any special instances where a function will have more than two horizontal asymptotes?

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- Jul 20th 2012, 06:06 AMLiberalArtMajorTakingCalcFunctions with more than two horizontal asymptotes?
Are there any special instances where a function will have more than two horizontal asymptotes?

- Jul 20th 2012, 06:51 AMskeeterRe: Functions with more than two horizontal asymptotes?
a single horizontal asymptote occurs when $\displaystyle \lim_{x \to \pm \infty} f(x) = L$

it is possible for two to exist ...

$\displaystyle \lim_{x \to \infty} f(x) = L$

$\displaystyle \lim_{x \to -\infty} f(x) = K$

$\displaystyle K \ne L$

if there were three, then neither of the above limits would exist. - Jul 20th 2012, 06:55 AMPlatoRe: Functions with more than two horizontal asymptotes?
Do you know the

for a function?**vertical line test**

What would more than two horizontal asymptotes imply?

Have a look at this. - Jul 20th 2012, 07:03 AMLiberalArtMajorTakingCalcRe: Functions with more than two horizontal asymptotes?
I already know all of that, but I haven't learned multivariate or vector calculus yet and I was wondering if there are any functions in the upper-division mathematics that have more than two

- Jul 20th 2012, 07:15 AMHallsofIvyRe: Functions with more than two horizontal asymptotes?
Your question has nothing to do with "multivariable or vector Calculus", it has only to do with the

**definition**of "horizontal asymptote".

If you want to ask your question in terms of multiple independent variables, you will have to**define**"horizontal" an "horizontal asymptote" in multiple variables.