 # Objectives: Find the domain of a Rational Function Determine the Vertical Asymptotes of a Rational Function Determine the Horizontal or Oblique Asymptotes.

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Objectives: Find the domain of a Rational Function Determine the Vertical Asymptotes of a Rational Function Determine the Horizontal or Oblique Asymptotes of a Rational Function

 A quotient of polynomial functions where are polynomial functions and. The domain is the set of all real numbers except those for which the denominator is 0.  EX: Find the domain of each rational function  1.2.  3.

 1.2.

 A graph will never intersect a vertical asymptote but may intersect a horizontal or oblique.  Locating Asymptotes:  Vertical: factor the numerator and denominator, cancel out the common factors and find the zeros of the denominator  The degree of the numerator is n and the degree of the denominator is m.  1. If, the x-axis or is the horizontal asymptote  2. If, the line the horizontal asymptote  3. If, the lineis the oblique asymptote  4. If, the graph has no horizontal or oblique asymptote  The graph of a rational function either has one horizontal or one oblique asymptote or else has no horizontal and no oblique asymptote

 1.2.  3.4.

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