...have more than two horizontal asymptotes?

I just want to know for sure.

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- Feb 5th 2008, 04:58 PMadhesiveWhy can't a graph...
...have more than two horizontal asymptotes?

I just want to know for sure. - Feb 5th 2008, 05:30 PMmr fantastic
You find horizontal asymptotes by considering the limiting behavior of y = f(x) as x approaches +oo and -oo:

If $\displaystyle \lim_{x \rightarrow -\infty} f(x) = a$ then $\displaystyle y \rightarrow a$ and the line $\displaystyle y = a$ is a horizontal asymptote.

If $\displaystyle \lim_{x \rightarrow +\infty} f(x) = b$ then $\displaystyle y \rightarrow b$ and the line $\displaystyle y = b$ is a horizontal asymptote.

When they exist, the values of a and b are unique by the 'uniquesness of a limit theorem'.

Therefore there are no more than two possible horizontal asymptotes.

Stick at it (Rofl)