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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.
     
  2. jcsd
  3. Oct 15, 2012 #2

    HallsofIvy

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    You just need a fraction in which the numerator has degree three more than the denominator. And example is [itex](x^4- 1)/(x+ 1)[/itex]. Dividing both numerator and denominator by x we have [itex](x^3- (1/x))/(1+ (1/x))[/itex] which approaches [itex]x^3[/itex] as x goes to infinity or negative infinity.
     
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