8.2 Graph Simple Rational Functions

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8.2 Graph Simple Rational Functions
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Rational Function

• A function of the form
• where p(x) q(x) are polynomials and q(x)?0.

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Hyperbola
x0

• A type of rational function.
• Has 1 vertical asymptote and 1 horizontal
  asymptote.
• Has 2 parts called branches. (blue parts) They
  are symmetrical.
• Well discuss 2 different forms.

y0
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Hyperbola (continued)

• One form
• Has 2 asymptotes xh (vert.) and yk (horiz.)
• Graph 2 points on either side of the vertical
  asymptote.
• Draw the branches.

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Hyperbola (continued)

• Second form
• Vertical asymptote Set the denominator equal to
  0 and solve for x.
• Horizontal asymptote
• Graph 2 points on either side of the vertical
  asymptote. Draw the 2 branches.

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Ex Graph State the domain range.
Vertical Asymptote x1 Horizontal Asymptote y2
x y -5 1.5 -2 1 0 -1 4 3
Left of vert. asymp.
Right of vert. asymp.
Domain all real s except 1. Range all real
s except 2.
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Ex GraphState domain range.

• Vertical asymptote
• 3x30 (set denominator 0)
• 3x-3
• x -1
• Horizontal Asymptote

x y -3 .83 -2 1.33 0 -.67 2
0
Domain All real s except -1. Range All real
s except 1/3.