1. Quote of the Day
What is now proved was once only imagined. -William Blake

2. Graph Rational Functions
Section 12.2

3. Objectives:
Graph rational functions

4. Key Vocabulary: Rational function Hyperbola Branches of a hyperbola
Asymptotes of a hyperbola

5. Rational Function
The inverse variation function is a type of rational function. A rational function has a rule given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0.

6. Parent Rational Function

7. Example 1:
Compare the red graph to the parent graph (blue).

8. Example 2:
Graph the function. Identify its domain and range and compare the graph to the parent graph.

9. Example 3:
Graph the function. Identify its domain and range and compare the graph to the parent graph.

10. #1: Graph the function. Identify its domain and range
#1: Graph the function. Identify its domain and range. Compare the graph with the parent graph.

11. #2: Graph the function. Identify its domain and range
#2: Graph the function. Identify its domain and range. Compare the graph with the parent graph.

12. #3: Graph the function. Identify its domain and range
#3: Graph the function. Identify its domain and range. Compare the graph with the parent graph.

13. #4: Describe how the graphs are related.

14. Graphing Rational Functions

15. Example 4:
Graph the function.

16. #5: Graph the function.

17. #6: Complete.
For which function is the domain all real numbers except -3 and the range all real numbers except 7? .

18. Example 5:
Your art club is planning a bus trip to an art museum. The cost for renting a bus is $495, and the cost will be divided equally among the people who are going on the trip. A museum ticket costs $12.50 per person.
Write an equation that gives the cost C (in dollars per person) of the trip as a function of the number of people p going on the trip.
Graph the equation. Describe the change in the cost as the number of people increases.
Use the graph to approximate the number of people who need to go on the trip so that the cost is about $25 per person.

19. Partner Work
Page 779 #4, 10, 16, 22, 30, 33

20. Homework Assignment Page 779 #6, 8, ,12, 14, 18, 20, 24, 26, 28
32, 34, 40, 46, 48, 56, 58, 60