1. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 1 ACT Practice Notes 1. Ms. Lewis plans to drive 900 miles to her vacation destination, driving an average of 50 miles per hour. How many miles per hour faster must she average, while driving, to reduce her total driving time by 3 hours? 2. The diameter, d centimeters, of the metal poles Goodpole Manufacturing produces must satisfy the inequality. What is the maximum diameter, in centimeters, such a metal pole may have?

2. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 2 Homework Answers 6a. See graphing calculator 6b. Your answers may vary but, using the points (18, 170) and (40, 324) you get: y = 7x + 44 6c. Calculator gives you: y = 7.57x + 33.38 with a correlation coefficient of about.88 6d. Prediction: 154 since r is close to 1

3. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 3 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%

4. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 4 Piecewise Functions This is an example of a piecewise function. For piecewise functions, different equations are used for different intervals of the domain.

5. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 5 Another Example Graph f(x) = 1 if 2 + x if 2x if x > 3

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

7. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 7 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.

8. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 8 Example of a Step/Greatest Integer Functon Xf(x) -3 -2 0 1 2 3 4

9. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 9 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%

10. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 10 Absolute Value Functions Really another special case of a piecewise function. Graph: f(x) = 2|x| - 6

11. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 11 Homework for Section 1-7 page 49, problems 14, 16, 18,and 26

12. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 12 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.

13. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 13 Examples Graph x > 3

14. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 14 Another Example Graph

15. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 15 Yet Another Example Graph y > |x – 2|

16. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 16 You Try Graph x – 2y < 8

17. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 17 You Try Graph

18. Objective: 1-6 and 1-7 Piecewise and Absolute Value Functions, Graphing Inequalities 18 Homework for Section 1-8 page 55, problems 12, 16, and 20