9.3 Rational Functions and Their Graphs

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9.3 Rational Functions and Their Graphs
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• If the graph is not continuous at x a then the
  function has a point of discontinuity at x a.

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Ex 1Find any points of discontinuity.
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Ex 2Find any points of discontinuity.
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Vertical Asymptotes

• There is a point of discontinuity for each real
  zero of Q(x).
• If P(x) and Q(x) have no common real zeros, then
  the graph has a VA at each real zero of Q(x).
• If P(x) and Q(x) have a common real zero, a, then
  there is a hole in the graph or a VA at x a.

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Ex 3Find the VA or holes.
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Ex 4Find the VA or holes.
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Ex 5Find the VA or holes.
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Horizontal Asymptotes(There is at most 1 HA per
graph.)

• If the degree of the denominator is gt the degree
  of the numerator then there is a HA at y 0.
• If the degree of the numerator is gt the degree of
  the denominator then there is NO HA.
• If the degree of the numerator the degree of
  the denominator then the HA is y a/b where a is
  the leading coefficient of the numerator b is
  the LC of the denominator.

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Ex 6Find the VA, HA, and holes.
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Ex 7Sketch the graph and identify the VA, HA,
and holes.
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• The zero of the numerator is the x-intercept!!