I know how to find the oblique/slant asymptote of a rational function. What I'm unsure about, because I've never dealt with this, is how many oblique asymptotes can a function actually have? And is it only possible to have an asymptote if the degree of the numerator polynomial and the degree of the denominator polynomial only differ by 1?

  • 2
    $\begingroup$ Aren’t you really asking about rational functions, i.e. quotients of two polynomials? Seems to me that a polynomial function doesn’t have any asymptote at all, except in the trivial case of degree one. $\endgroup$ – Lubin Dec 3 '13 at 2:34
  • $\begingroup$ Yes, a rational function...sorry. $\endgroup$ – mepinon Dec 3 '13 at 2:39

Those are actually called rational functions. An Oblique asymptote for one of those is the same at $\pm \infty.$

For other functions you can have two distinct oblique asymptotes, $$ \frac{\sqrt{1 + x^6}}{1 + x^2} $$ is roughly $|x|.$

Oh, my original point: you get at most two oblique asymptotes, because you are asking about the graph of a function.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.