Horizontal Asymptotes and Oblique Asymptotes

Example #1

  • to find the horizontal asymptote, there are three cases:
  • CASE 1: degree of numerator < degree of denominator
    • horizontal asymptote is y = 0


Example #2

  • CASE 2: degree of numerator = degree of denominator
    • horizontal asymptote is leading coefficient of numerator / leading coefficient of denominator


Example #3

  • CASE 3: degree of numerator > degree of denominator (more specifically, numerator degree is one higher than denominator degree)
    • first, factor and cancel if possible to check if there is a point of discontinuity (which won't have any horizontal asymptote)
    • if not, there is an oblique asymptote, divide numerator by denominator, asymptote = quotient

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