Lesson 2-7: Graphing Rational Functions

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Lesson 2-7 Graphing Rational Functions

• Advanced Math Topics

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Definitions

• Continuity a graph that is able to be traced
  without picking up the pencil
• Asymptote a line that the graph of the function
  approaches, but never touches (graphed as a
  dotted line)
• Point discontinuity a hole in the graph

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Vertical Asymptote
To find a vertical asymptote set the denominator
factor(s) equal to zero and solve
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Horizontal Asymptote
To Find A Horizontal asymptote look at the
degrees of the numerator and denominator If
the degree of the denominator is greater than
the degree of the numerator, then the
horizontal asymptote is y0 If the degree
of the denominator is equal to the degree of the
numerator then the horizontal asymptote is found
by dividing the coefficients of the leading
terms.
y1, is the horizontal asymptote because the
coefficients of the leading terms 1
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Point Discontinuity
Point discontinuity happens when you factor the
numerator and denominator and the denominator
factor is canceled. The value of x that makes
the denominator zero is the point of
discontinuity.
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• Evaluate Rational Functions just like you would
  any other function. Finding f(4) simply means
  plug 4 in for x.
• When you are looking for x and you know f(x)
  some then you replace the f(x) in function
  notation with the you are given and solve for x

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Find f(-4) and then find x when f(x) 2
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Word Problems

• Roy took two tests and his average is 63. If he
  scores 100 on the rest of his tests, how many
  more tests does Roy need to take to raise his
  average to 85?

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Steps to Graph a Rational Function

• 1. Factor and simplify if you can
• 2. Look for the vertical asymptote and horizontal
  asymptote
• 3. Draw asymptotes as dotted lines on your graph
• 5. Find 3 x values greater than the vertical
  asymptote and 3 less than the vertical asymptote
• ( If there is no vertical asymptote you must make
  a t-chart and find at least 5 points to sketch
  the graph)
• 6. graph the points and stretch the curve toward
  the asymptotes.

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Graphing Rational Functions
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Graphing Rational Functions

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Graphing Rational Functions

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Graphing Rational Functions