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A rational function has an oblique asymptote when the degree of its numerator

  • A.falls short of that of its denominator by one
  • B.exceeds that of its denominator by two or more
  • C.exceeds that of its denominator by exactly one
  • D.equals that of its denominator

Answer: C

Dividing out leaves a linear quotient plus a remainder that dies away, so the curve approaches a slant line. Equal degrees give a horizontal asymptote at the ratio of leading coefficients, a smaller numerator gives \( y = 0 \), and an excess of two or more gives a parabolic or higher approach with no straight asymptote at all

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