Rational Functions and Asymptotes

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Section 2.6
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Rational Functions and Asymptotes

• A rational function is a function written in the
  form of a polynomial divided by a polynomial.
• Domain is the x-values
• Remember you cannot have a zero in the
  denominator of a fraction

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Rational Functions and Asymptotes

• Vertical Asymptotes To find the vertical
  asymptotes set the denominator equal to zero and
  solve for x.
• Horizontal Asymptotes To find the horizontal
  asymptotes compare the degree of the numerator to
  the degree of the denominator.

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Rational Functions and Asymptotes

• Horizontal Asymptotes
• If the degree of the numerator is bigger than the
  degree of the denominator, then there is not a
  horizontal asymptote.
• If the degree of the numerator and the degree of
  the denominator are the same, then the horizontal
  asymptote is y leading coefficient over leading
  coefficient.

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Rational Functions and Asymptotes

• Horizontal Asymptotes
• If the degree of the denominator is bigger than
  the degree of the numerator, then the horizontal
  asymptote is y 0
• Asymptotes are equations
• Vertical Asymptotes are x
• Horizontal Asymptotes are y