Thread: Finding horizontal and vertical asymptotes, and telling the difference

1. Finding horizontal and vertical asymptotes, and telling the difference

I have a problem here:

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

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!

2. Originally Posted by qcom
I have a problem here:

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

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!
Since $\displaystyle y = \frac{x}{x-1} = \frac{(x - 1) + 1}{x-1} = 1 + \frac{1}{x-1}$ it should be evident (from what you have learned?) that the horizontal asymptote is y = 1.

3. Why are you taking these steps?

My teacher did not explain it well.

4. 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 $y = \frac{a}{bx + c} + d$ ?

5. 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.

6. Do you undersrtand what "vertical" and "horizontal" mean here? Do you understand which axis is the "x" axis and which the "y" axis?

7. 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.

8. Originally Posted by qcom
Yes! Of course I do.
Excellent! Then why are you asking how to distinguish "vertical asymptotes" from "horizontal asymptotes"?