Thread: Finding asymptotes

How do I find all of the asymptotes (vertical, horizontal, oblique) of the function (x^3 + 1) / (x^2 - 2x + 2) ? For the vertical asymptote I believe it's 1 + i but I'm not too sure about that. Can anyone help me out with that asymptote and whatever other asymptotes this formula might have? Thanks!

Originally Posted by Hamzawesome

How do I find all of the asymptotes (vertical, horizontal, oblique) of the function (x^3 + 1) / (x^2 - 2x + 2) ? For the vertical asymptote I believe it's 1 + i but I'm not too sure about that. Can anyone help me out with that asymptote and whatever other asymptotes this formula might have? Thanks!

Since is defined for all it follows that has no vertical asymptote .

Since it follows that has no horizontal asymptote .

However , could has an oblique asymptote...

How did you come up with the answer of 1+i? Are you aware that it is a complex root of denominator?

You can find the oblique asymptote by using synthetic division and disregarding the remainder since the denominator is one degree less than the numerator.

Originally Posted by princeps

Since is defined for all it follows that has no vertical asymptote .

Since it follows that has no horizontal asymptote .

However , could has an oblique asymptote...

For the oblique asymptote I got y=x+1, after using long division. But for the vertical and horizontal asymptotes I just got "none" as you inferred.

You're oblique asymptote is not correct, normally it has to be , recheck your calculations about