1. Piecewise-Defined Functions
Lesson 2.5

2. Piecewise Defined Functions
Consider a function defined differently for different parts of the domain (the x values)
Consider what the table of values looks like

3. Piecewise Defined Functionsx y -1 1 2 3 4

4. Piecewise Defined Functions
Our calculator handles piecewise functions with the when ( ) command
What will the graph look like?
Use Diamond 0 for the ≤ sign

5. Piecewise Defined Functions

6. Piecewise Defined Functions
Condition
Expression to use when condition is true
Expression to use when condition is false

7. Piecewise Defined Functions
Try entering and graphing the following function

8. Piecewise Defined Functions

9. Absolute Value Function
Whatever you put into the function comes out positive -3 +7 +7 +3

10. Absolute Value Function
Definition
Use the abs( ) function on your calculator

11. Absolute Value Function
Note the graph of y = | x |
Table of values

12. Absolute Value Inequalities
|a x + b | < k is equivalent to
- k < a x + b < k
- k < a x + b and a x + b < k 7

13. Absolute Value Inequalities
|a x + b | > k is equivalent to
a x + b < -k or a x + b > k 7 ) )

14. Try It Out! |15 – x | < 7 |5x – 7 | > 2 Solve symbolically
Show graphical solution

15. Assignment
Lesson 2.5
Page 133
Exercises 1 – 77 EOO