Graphing Rational Functions

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• Graphing Rational Functions

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Rational Function

• Where N(x) is the numerator polynomial and D(x)
  is the denominator polynomial.
• Domain all real numbers except where the
  denominator equals zero.
• Parent Function - ,
• where

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RATEY tool to graph rational functions

• R roots ? where
• A asymptotesvertical ? set
• T togetherness ? determine the direction of
• the branches by picking test points
  around the
• asymptotes
• E end behaviorhorizontal asymptotes
• Y y-intercepts ? set and solve for y

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Vertical Asymptotes

• Set the denominator equal to zero.
• Solve for x.
• Written as x

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Horizontal Asymptotes

• Identify the highest power in the numerator
  denominator.
• If the numerator power is higher than the
  denominator power, then there is no horizontal
  asymptote.
• If the numerator power is equal to the
  denominator power, then the horizontal asymptote
  is the coefficients in front of the highest
  powers (y a/b).
• If the numerator power is lower than the
  denominator power, then the horizontal asymptote
  is y O.

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Horizontal Asymptotes

• N(x) gt D(x) ? no horizontal asymptote
• N(x) D(x) ? y a/b
• N(x) lt D(x) ? y O

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Graph the Rational FunctionStep I Factor and
find all the informationEx 1.

• R- roots
• A vertical asymptotes
• T togetherness
• E horizontal asymptotes
• Y y-intercepts

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Graph the Rational FunctionStep II Graph using
the informationyou found in Step IEx 1.
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Graph the Rational FunctionStep I Factor and
find all the informationEx 2.

• R- roots
• A vertical asymptotes
• T togetherness
• E horizontal asymptotes
• Y y-intercepts

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Graph the Rational FunctionStep II Graph using
the informationyou found in Step IEx 2.
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Writing Equations of a Rational FunctionsEx. 3
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Writing Equations of a Rational FunctionsEx. 4