1. Section 3.5 Rational Functions and Their Graphs

2. Rational Functions

4. Example
Find the domain of the rational function.

5. Example
Find the domain of the rational function.

6. Vertical Asymptotes of Rational Functions

11. Two Graphs with Vertical Asymptotes, one without

12. Graphing Calculator
Connected mode
Dot Mode

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

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

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

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

17. Horizontal Asymptotes of Rational Functions

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

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

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

22. Using Transformations to Graph Rational Functions

23. Graphs of Common Rational Functions

24. Transformations of Rational Functions

25. Example

26. Example

27. Graphing Rational Functions

29. Example

30. Example

31. Slant Asymptotes

33. Example

34. Example

35. Applications

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.

38. (a)
(b)
(c)
(d)

39. (a)
(b)
(c)
(d)

40. (a)
(b)
(c)
(d)