Warm up

1. Warm up • Graph f(x) = 2|x -3|-1

2. Lesson Piecewise Functions Objective: To be able to graph piecewise functions.

3. Up to now, we’ve been looking at functions represented by a single equation. • In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. • These are called piecewise functions.

4. Up to now, we’ve been looking at functions represented by a single equation. • In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. • These are called piecewise functions.

5. One equation gives the value of f(x) when x ≤ 1 • And the other when x>1

6. Graph: • For all x’s < 1, use the top graph (to the left of 1) • For all x’s≥ 1, use the bottom graph (to the • right of 1)

7. x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.

8. Graph

9. Step Functions

11. Evaluating a Piecewise Function

12. Solution part a

13. Solution part a

14. Solution part c

15. Practice Exercise

16. Answer

17. Graphing a piecewise function on a calculator http://mathbits.com/MathBits/TIsection/Precalculus/piecewise.htm

18. Sources blogs.harrisonhigh.org/dennis_attaway/2.5---piecewise-functions.ppt http://mathbits.com/MathBits/TIsection/Precalculus/piecewise.htm