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Can there be cubic asymptotes in rational functions

  1. Oct 14, 2012 #1
    I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.
    1. The problem statement, all variables and given/known data
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 14, 2012 #2

    LCKurtz

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    What is a "cubic" asymptote?
     
  4. Oct 14, 2012 #3
    im not really sure, but we have to figure it out. Its like vertical, horizontal and oblique asymptotes in rational function. I have to figure out if there could be a cubic asymptote. I know that there could be a quadratic asymptote, but im not sure about cubic.
     
  5. Oct 14, 2012 #4

    LCKurtz

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    Then, what is a "quadratic" asymptote? Those terms is unfamiliar to me regarding asymptotes.
     
  6. Oct 14, 2012 #5
    A quadratic asymptote is an asymptote on a rational function which looks like a parabola. So if you are graphing a rational function with a quadratic asymptote is doesnt pass through. Just like the oblique, vertical and horizontal asymptotes.
     
  7. Oct 14, 2012 #6

    LCKurtz

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    Asymptotes don't "look like parabolas". They are straight lines. And I am certain your text doesn't define a quadratic asymptote as one that "looks like a parabola". Tell me, word for word, what your text definition of a quadratic asymptote is. How can you hope to solve a problem if you don't know the definitions?
     
  8. Oct 14, 2012 #7
    For example 2x^3/x-1, when you divide 2x^3 by x-1 you will get a quadratic function, when you graph that function, that will be the quadratic asymptote.
     
  9. Mar 8, 2013 #8
    I found an example of a cubic asymptote on http://www.webgraphing.com/graphing_basic.jsp [Broken]
    The rational function was f(x)= (2x^4)/(x-1).
    Now I am curious if you can have asymptotes of any degree...
     
    Last edited by a moderator: May 6, 2017
  10. Mar 8, 2013 #9

    Mark44

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    I haven't run across this term (cubic asymptote) before, but I would guess that it means that for large |x|, the graph approaches that of some cubic polynomial.
     
  11. Mar 8, 2013 #10

    LCKurtz

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    Yes, that is the obvious guess, and similarly for a "quadratic" asymptote. But it annoys me when posters won't look up definitions in their own texts and instead abandon the thread as jann95 has apparently done.
     
  12. May 1, 2013 #11
  13. May 1, 2013 #12

    HallsofIvy

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    No, and asymptote does NOT have to be a straight line. Any curve can be an asymptote to a graph. The only requirement is that the graph, as x-> a, must get arbitrarily close to the curve without reaching it.
     
  14. May 1, 2013 #13

    LCKurtz

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    To quote from Wikipedia which, as we all know, is the ultimate source of correctness in mathematics :uhh::

    "More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes."
     
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