# Finding horizontal and vertical asymptotes, and telling the difference

• Sep 21st 2010, 03:10 PM
qcom
Finding horizontal and vertical asymptotes, and telling the difference
I have a problem here:

$\displaystyle f(x) = x/(x-1)$

How can I tell whether this has a vertical or horizontal asymptotes?

I can tell that X cannot = 1, but this is vertical, correct?

How do I tell better? I'm a little confused, but willing to learn! :D
• Sep 21st 2010, 03:14 PM
mr fantastic
Quote:

Originally Posted by qcom
I have a problem here:

$\displaystyle f(x) = x/(x-1)$

How can I tell whether this has a vertical or horizontal asymptotes?

I can tell that X cannot = 1, but this is vertical, correct? Mr F says: Yes.

How do I tell better? I'm a little confused, but willing to learn! :D

Since $\displaystyle \displaystyle y = \frac{x}{x-1} = \frac{(x - 1) + 1}{x-1} = 1 + \frac{1}{x-1}$ it should be evident (from what you have learned?) that the horizontal asymptote is y = 1.
• Sep 21st 2010, 03:25 PM
qcom
Why are you taking these steps?

My teacher did not explain it well.
• Sep 21st 2010, 03:27 PM
mr fantastic
Quote:

Originally Posted by qcom
Why are you taking these steps?

My teacher did not explain it well.

Have you not been taught about functions (called hyperbolas) of the form $\displaystyle y = \frac{a}{bx + c} + d$ ?
• Sep 21st 2010, 03:28 PM
qcom
I do know about hyperbolas a little from last year, but I don't remember them being in this form, although I can probably work with them like this.
• Sep 22nd 2010, 02:06 AM
HallsofIvy
Do you undersrtand what "vertical" and "horizontal" mean here? Do you understand which axis is the "x" axis and which the "y" axis?
• Sep 22nd 2010, 05:54 AM
qcom
Quote:

Originally Posted by HallsofIvy
Do you undersrtand what "vertical" and "horizontal" mean here? Do you understand which axis is the "x" axis and which the "y" axis?

Yes! Of course I do.
• Sep 23rd 2010, 03:27 AM
HallsofIvy
Quote:

Originally Posted by qcom
Yes! Of course I do.

Excellent! Then why are you asking how to distinguish "vertical asymptotes" from "horizontal asymptotes"?