1. Section4.2 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. Example Find the vertical asymptote, if any, of the graph of the rational function.

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

16. Horizontal Asymptotes of Rational Functions

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

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

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

21. Using Transformations to Graph Rational Functions

22. Graphs of Common Rational Functions

23. Transformations of Rational Functions

25. Graphing Rational Functions

27. Example

29. Slant Asymptotes

31. Example

33. Applications

35. (a) (b) (c) (d)

36. (a) (b) (c) (d)

37. (a) (b) (c) (d)