1. Graphing Rational Expressions

2. Find the domain:
Graph it:

3. Find the domain:
Graph it:

4. Vertical Asymptote
If (x – a) is a factor of the denominator of a rational function but not a factor of the numerator, then x = a is a vertical asymptote of the graph of the function.

5. Find the domain:
Graph it using the graphing calculator:

6. Hole (in the graph)
If (x – b) is a factor of both the numerator and denominator of a rational function, then there is a hole in the graph of the function where x = b, unless x = b is a vertical asymptote.
The exact point of the hole can be found by plugging b into the function after it has been simplified.

7. Find the domain and identify vertical asymptotes & holes.

8. Find the domain and identify vertical asymptotes & holes.

9. Find the domain and identify vertical asymptotes & holes.

10. Find the domain and identify vertical asymptotes & holes.

11. Horizontal Asymptotes
Degree of numerator = Degree of denominator
Degree of numerator < Degree of denominator
Degree of numerator > Degree of denominator
Horizontal Asymptote:
Horizontal Asymptote:
Horizontal Asymptote:

12. Find all asymptotes & holes & then graph:

13. Find all asymptotes & holes & then graph:

14. Find all asymptotes & holes & then graph:

15. Find all asymptotes & holes & then graph:

16. Find all asymptotes & holes & then graph:

17. Find all asymptotes & holes & then graph:

18. Find all asymptotes & holes & then graph:

19. Find all asymptotes & holes & then graph: