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Vertical Asymptote Horizontal Asymptote x = 4 y = 1 Hole At x = -2
[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Example 3-1a Undefined for  x  = –2  and  –3 Hole at x = -2 Vertical asymptote is the line x = -3 Horizontal asymptote: the line y = 1  Determine the equations of any asymptotes and the values of  x  for any holes in the graph of
Graph VA:  x = -3 HA:  y = 1 Hole at x = -2 -2 -2 = -4 (-2, -4)
Graph x -6 -5 -4 -1 0 1 -8/-3  or 8/3 -7/-2  or  7/2 -6/-1  or 6 -3/2 -2/3 -1/4
Example 3-2a VA:  x  = –1 No holes HA: y = 1   Graph
Example 3-2b x f   ( x ) – 4 -4/-3 = 4/3 – 3 -3/-2 = 3/2 – 2 -2/-1 = 2 0 0/1 = 0 1 1/2 2 2/3 3 3/4 Graph
Example 3-3a Undefined for  x  = 2   Hole at x = 2 2 (2, 4) x -1 0 1 1 2 3 Graph

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Alg2 Lesson 9 3

  • 1. Vertical Asymptote Horizontal Asymptote x = 4 y = 1 Hole At x = -2
  • 2.
  • 3.
  • 4. Example 3-1a Undefined for x = –2 and –3 Hole at x = -2 Vertical asymptote is the line x = -3 Horizontal asymptote: the line y = 1 Determine the equations of any asymptotes and the values of x for any holes in the graph of
  • 5. Graph VA: x = -3 HA: y = 1 Hole at x = -2 -2 -2 = -4 (-2, -4)
  • 6. Graph x -6 -5 -4 -1 0 1 -8/-3 or 8/3 -7/-2 or 7/2 -6/-1 or 6 -3/2 -2/3 -1/4
  • 7. Example 3-2a VA: x = –1 No holes HA: y = 1 Graph
  • 8. Example 3-2b x f ( x ) – 4 -4/-3 = 4/3 – 3 -3/-2 = 3/2 – 2 -2/-1 = 2 0 0/1 = 0 1 1/2 2 2/3 3 3/4 Graph
  • 9. Example 3-3a Undefined for x = 2 Hole at x = 2 2 (2, 4) x -1 0 1 1 2 3 Graph