1. Section 3.5 Rational Functions and Their Graphs

3. Example
Find the domain of the rational function.

4. Example
Find the domain of the rational function.

5. Vertical Asymptotes of Rational Functions

10. Two Graphs with Vertical Asymptotes, one without

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

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. 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.

15. Horizontal Asymptotes of Rational Functions

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

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

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

20. Using Transformations to Graph Rational Functions

21. Graphs of Common Rational Functions

22. Transformations of Rational Functions

23. Example

24. Graphing Rational Functions

26. Example

27. Example

28. Slant Asymptotes

30. Example

31. Example

32. Applications

33. (a)
(b)
(c)
(d)

34. (a)
(b)
(c)
(d)

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