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Section 3.5 Rational Functions and Their Graphs

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.

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Section 3.5 Rational Functions and Their Graphs

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  1. Section 3.5Rational Functions and Their Graphs

  2. Rational Functions

  3. Example Find the domain of the rational function.

  4. Example Find the domain of the rational function.

  5. Vertical Asymptotes of Rational Functions

  6. Two Graphs with Vertical Asymptotes, one without

  7. Graphing Calculator Connected mode Dot Mode

  8. Example Find the vertical asymptote, if any, of the graph of the rational function.

  9. Example Find the vertical asymptote, if any, of the graph of the rational function.

  10. Example Find the vertical asymptote, if any, of the graph of the rational function.

  11. A graph with a hole corresponding to the denominator’s zero. Your calculator will not show the hole.

  12. Horizontal Asymptotes of Rational Functions

  13. Two Graphs with Horizontal Asymptotes, one without Notice how the horizontal asymptote intersects the graph.

  14. Example Find the horizontal asymptote, if any, of the graph of the rational function.

  15. Example Find the horizontal asymptote, if any, of the graph of the rational function.

  16. Using Transformations to Graph Rational Functions

  17. Graphs of Common Rational Functions

  18. Transformations of Rational Functions

  19. Example

  20. Example

  21. Graphing Rational Functions

  22. Example

  23. Example

  24. Slant Asymptotes

  25. Example

  26. Example

  27. Applications

  28. 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. (a) (b) (c) (d)

  30. (a) (b) (c) (d)

  31. (a) (b) (c) (d)

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