1. Warm Up Graph the following functions on the same coordinate plane:

2. Answers Graph the following functions on the same coordinate plane:

3. Think about the name “Piecewise Functions.” What do you think we will be doing in this unit?

4. Piecewise Functions Piecewise functions are neighbors! Their properties are separated by a fence.

5. Example 1 1 1 2 2 It’s in two pieces! Each piece must live ONLY in its own neighborhood. Let’s put up a fence, so we don’t make any mistakes! These number(s) tell us where to put a fence.

6. Example 1 These number(s) tell us where to put a fence. lives here Now, we need to figure out who the fence owner is. This guy has the “=”, so he gets to sit ON the fence. 1 1 2 2

7. Example 1 Let’s graph part 1. This guy has the “=”, so he gets to sit ON the fence. 1 1 2 2 He does not get to sit on the fence.

8. Example 1 This guy has the “=”, so he gets to sit ON the fence. 1 1 2 2 Let’s graph part 2. Since he owns the fence, he can sit on it.

9. Example 2 f(x) = x 2 + 1 if x  0 x – 1 if x  0

10. Example 3 3x + 2 if x  -2 -x if -2  x  1 x 2 – 2 if x  1 f(x) =

11. x 2 + 1 if x  0 x – 1 if x  0 Let’s calculate f(2). There are two functions here! How do we know which one to use to evaluate f(2)? Example 4

12. f(x) = 2x + 1 if x  0 2x + 2 if x  0 Evaluate the following: f(-2) =-3? f(0) =2? f(5) =12 ? f(1) =4? Example 5

13. f(x) = 3x – 2 if x  -2 -x if -2  x  1 x 2 – 7x if x  1 Evaluate the following: f(-2) =2? f(-4) =-14? f(3) =-12 ? f(1) =-6 ? Example 6

14. Homework Evaluating & Graphing Piecewise Functions Worksheet