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Section 3.5 Rational Functions  and  Their Graphs
Rational Functions
 
Example Find the domain of the rational function.
Example Find the domain of the rational function.
Vertical Asymptotes of  Rational Functions
 
 
 
 
Two Graphs with Vertical Asymptotes, one without
Graphing Calculator Connected mode Dot Mode
Example Find the vertical asymptote, if any, of the graph of the rational function.
Example Find the vertical asymptote, if any, of the graph of the rational function.
Example Find the vertical asymptote, if any, of the graph of the rational function.
A graph with a hole corresponding to the denominator’s zero.  Your calculator will not show the hole.
Horizontal Asymptotes of Rational Functions
 
Two Graphs with Horizontal Asymptotes, one without Notice how the horizontal asymptote intersects the graph.
Example Find the horizontal asymptote, if any, of the graph of the rational function.
Example Find the horizontal asymptote, if any, of the graph of the rational function.
Using  Transformations to Graph Rational Functions
Graphs of Common Rational Functions
Transformations of Rational Functions
Example
Example
Graphing Rational Functions
 
Example
Example
Slant Asymptotes
 
Example
Example
Applications
 
Example The Fort Myers Fishing Company discovered a better material for making fishing reels.  The fixed monthly cost is  ...
(a)  (b) (c) (d)
(a)  (b) (c) (d)
(a)  (b) (c) (d)
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Transcript of "3"

  1. 1. Section 3.5 Rational Functions and Their Graphs
  2. 2. Rational Functions
  3. 4. Example Find the domain of the rational function.
  4. 5. Example Find the domain of the rational function.
  5. 6. Vertical Asymptotes of Rational Functions
  6. 11. Two Graphs with Vertical Asymptotes, one without
  7. 12. Graphing Calculator Connected mode Dot Mode
  8. 13. Example Find the vertical asymptote, if any, of the graph of the rational function.
  9. 14. Example Find the vertical asymptote, if any, of the graph of the rational function.
  10. 15. Example Find the vertical asymptote, if any, of the graph of the rational function.
  11. 16. A graph with a hole corresponding to the denominator’s zero. Your calculator will not show the hole.
  12. 17. Horizontal Asymptotes of Rational Functions
  13. 19. Two Graphs with Horizontal Asymptotes, one without Notice how the horizontal asymptote intersects the graph.
  14. 20. Example Find the horizontal asymptote, if any, of the graph of the rational function.
  15. 21. Example Find the horizontal asymptote, if any, of the graph of the rational function.
  16. 22. Using Transformations to Graph Rational Functions
  17. 23. Graphs of Common Rational Functions
  18. 24. Transformations of Rational Functions
  19. 25. Example
  20. 26. Example
  21. 27. Graphing Rational Functions
  22. 29. Example
  23. 30. Example
  24. 31. Slant Asymptotes
  25. 33. Example
  26. 34. Example
  27. 35. Applications
  28. 37. Example The Fort Myers Fishing Company discovered a better material for making fishing reels. The fixed monthly cost is $10,000 for the cost of rental of space, manufacturing equipment, as well as wages and benefits for it’s employees. It costs $10 for materials to make each fishing reel.
  29. 38. (a) (b) (c) (d)
  30. 39. (a) (b) (c) (d)
  31. 40. (a) (b) (c) (d)
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