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Alg2 lesson 9-3
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Alg2 lesson 9-3

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Transcript

  • 1. Vertical Asymptote
    x = 4
    Hole
    Horizontal Asymptote
    At x = -2
    y = 1
  • 2. Graphing rational functions
    Factor numerator and denominator
    Discontinuities occur where denominator equals zero
    • Holes are indicated by factors of denominator that cancel out
    • 3. Vertical asymptotes are indicated by factors of denominator that do not cancel
  • Horizontal Asymptotes (predict end behavior) – look at highest degree term of numerator and denominator
    • Degree of top > degree of bottom: no HA
    • 4. Degree of top < degree of bottom: HA is y = 0
    • 5. Degrees equal: HA is y =
  • Determine the equations of any asymptotes and the values of x for any holes in the graph of
    Undefined for x = –2 and –3
    Hole at x = -2
    Vertical asymptote is the line x = -3
    Horizontal asymptote:
    the line y = 1
    Example 3-1a
  • 6. Graph
    VA: x = -3
    HA: y = 1
    Hole at x = -2
    (-2, -4)
    -2
    = -4
    -2
  • 7. Graph
    x
    -8/-3 or 8/3
    -7/-2 or 7/2
    -6/-1 or 6
    -3/2
    -2/3
    -1/4
    -6
    -5
    -4
    -1
    0
    1
  • 8. Graph
    VA: x = –1
    No holes
    HA: y = 1
    Example 3-2a
  • 9. Graph
    Example 3-2b
  • 10. Graph
    Undefined for x = 2
    (2, 4)
    Hole at x = 2
    2
    x
    -1
    0
    1
    1
    2
    3
    Example 3-3a