1. Piecewise Functions

2. What is a piecewise function?
Piecewise Function is defined by at least two equations, each of which applies to a different part if the function’s domain.
Point of discontinuity – points on the graph of a function in which there is a break, hole or gaps.

3. What does the equation look like???
One equation gives the value of f(x) when x ≤ 1
And the other when x>1

4. Absolute functions as piecewise function
Look at the graph what can you make out of the absolute value???

5. Lets try again First identify the two lines. Write your domain
Write each equation to match the domains

6. Lets try again

7. Your turn!

8. Other Piecewise Functions
Write an equation for the following.

9. Write the equation to the following graph

10. Evaluate f(x) when x=0, x=2, x=4
First you have to figure out which equation to use
You NEVER use both
X=4
X=2
X=0
This one fits
into the top
equation
So:
0+2=2
f(0)=2
So:
2(4) + 1 = 9
f(4) = 9
This one fits here
So:
2(2) + 1 = 5
f(2) = 5
This one fits here

11. 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)

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

13. Graph:

14. Step Functions

16. Graph :

18. Assignment Classwork Homework Page 51 Page 52 # 1 – 11 all # 1 – 7 all
8 and 9

19. Assignment
Page 51
12 – 14 all
Page 52
8 and 9