1. 1 What you will learn today 1. How to evaluate piecewise functions 2. How to graph piecewise functions 3. How to determine piecewise functions from a graph

2. Objective: 2.7 Piecewise Functions 2 Piecewise Functions Up until this point, we have represented functions with one equation. In “real life” many situations can best be represented by a set of functions. Each function corresponds to a different part of the domain. These are called “piecewise functions”. We are going to learn to evaluate piecewise functions, graph them and write them.

3. Objective: 2.7 Piecewise Functions 3 Evaluating Example  Evaluate f(x) when a) x = 0 b) x = 2, and c) x = 4 given

4. Objective: 2.7 Piecewise Functions 4 You Try Evaluate f(x) when a) x = 0, b) x = 3, c) x = 6

5. Objective: 2.7 Piecewise Functions 5 Graphing a Piecewise Function  Graph

6. Objective: 2.7 Piecewise Functions 6 You Try  Graph

7. Objective: 2.7 Piecewise Functions 7 A Step Function A function that results in a graph that looks like a set of stairs. An example is the greatest integer function.

8. Objective: 2.7 Piecewise Functions 8 Graphing a Step Function  Graph

9. Objective: 2.7 Piecewise Functions 9 Writing a Piecewise Function  Write an equation for the piecewise function whose graph is shown.

10. Objective: 2.7 Piecewise Functions 10 You Try  Write an equation for the following graph.

11. Objective: 2.7 Piecewise Functions 11 A “Real World” Example  You have a summer job that pays time and a half for overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal wage of $7.  Write a piecewise function that gives you your weekly pay P in terms of the number of hours you work.  How much will you get paid if you work 45 hours?

12. Objective: 2.7 Piecewise Functions 12 Homework  Page 117, 14-20 even, 22, 26, 28, 38.