1. Piecewise Functions

2. Piecewise function Objectives: Evaluate piecewise functions
Graph Piecewise Functions
Graph Step Functions
Vocabulary: Piecewise Functions, Step Functions

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

4. Piecewise function
All piecewise functions start with:

5. Piecewise function
Since this one is in three parts, it will have three lines within f(x)

6. Piecewise function
This graph already tells us, the equation for each branch. The part we need to focus on is x = 2, where the graph splits.

7. Evaluate f(x) when x=0, x=2, x=4
First you have to figure out which equation to use.
You NEVER use both!
Then evaluate using that equation.
Now graph your equation.

8. Step Functions
Step Function: Type of Piecewise function. The output remains constant with in each branch and changes in value from one interval to the next.

9. Step Functions

10. Graph :

11. Graph: 1. Make a table for several values of each function
2. Graph those values
3. Remember your endpoints! Open or closed?

12. Graph:

13. Workbook page 12 #1-14
Pg. 13 shows how to put piecewise functions into your graphing calculator (TI-83 and TI-84)

14. Example with different boundary points
Make a table with a few points for each function.
ALWAYS plug in the boundary point(s) into BOTH functions (show on your table)
If the y-value for the boundary point(s) is the same in both functions, then just plot the point and keep going
If the y-value for the boundary point(s) is different in each function, then you plot both points- one should be open circled, one should be close circled

15. Example where the boundary points are the same
1.) 𝑓= 𝑥− 𝑥≤1 𝑥 2 −2𝑥 𝑥>1
2.) 𝑓= 𝑥 𝑥≤0 3 𝑥 2 −𝑥 𝑥>0

16. Graph : step function
It costs $1.40 for the first minute of a phone call to Paris, France, and $0.80 for each additional minute or fraction thereof. Draw a graph of a step function that models this cost. MAKE A TABLE FIRST!

17. Practice Sess
20 minutes
Workbook page 14-15

18. Bellringer: Write the piecewise function for each picture

19. Write An Equation for the Given Graph
Look for at least 2 points on each part of the graph
For linear functions, find the slope of the line using those 2 points Put into point-slope form
Keep in mind that horizontal lines are f(x)= #
WHER ARE YOUR BOUNDARIES AT??

20. Write An Equation for the Given Graph
(-3,0)
(2,2)

21. Homework!
Workbook pg all