1. 1 What you will learn  How to graph and identify piecewise functions  How to graph linear inequalities

2. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 2 Piecewise Functions  Imagine the following data set:  How do you graph that? Limits of IncomeTax Bracket 0 to 7000 0% 7001 to 28,400 15% 28,401 to 68,800 25% 68,801 to 143,500 28% 143,501 to 311,950 33% Over 311,950 35%

3. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 3 Piecewise Functions  This is an example of a piecewise function. For piecewise functions, different equations are used for different intervals of the domain.

4. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 4 Another Example  Graph f(x) = 1 if 2 + x if 2x if x > 3

5. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 5 You Try  On graph paper: Graph: 2 if f(x) = x + 4 if 2x if x > 4

6. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 6 Step Function  A piecewise function that looks like a set of stairs is called a step function. You can’t trace the graph of a step function without lifting your pencil.  A good example of a step function is the graph of a greatest integer function.

7. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 7 Example of a Step/Greatest Integer Function Xf(x) -3 -2 0 1 2 3 4

8. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 8 You Try  How would you graph the problem at the beginning of the slides? Limits of IncomeTax Bracket 0 to 7000 0% 7001 to 28,400 15% 28,401 to 68,800 25% 68,801 to 143,500 28% 143,501 to 311,950 33% Over 311,950 35%

9. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 9 Absolute Value Functions  Really another special case of a piecewise function. Graph: f(x) = 2|x| - 6

10. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 10 Homework for Section 1-7  page 49, problems 14, 16, 18,and 26

11. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 11 Graphing Linear Inequalities  Remember – 1. Graph the boundary line (dotted line for, solid if it is 2. Test a point. 3. Shade the “half plane” that includes the points that work in the inequality.

12. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 12 Examples  Graph x > 3

13. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 13 Another Example  Graph

14. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 14 Yet Another Example  Graph y > |x – 2|

15. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 15 You Try  Graph x – 2y < 8

16. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 16 You Try  Graph

17. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 17 Homework for Section 1-8  page 55, problems 12, 16, and 20