1. Piecewise Functions Lesson Talking Points Included
Algebra I
CCSS

2. An Absolute Value function is a famous piecewise function

3. An Absolute Value function is a famous piecewise function
It is made up of two pieces

4. It fails the vertical line test!
An Absolute Value function is a famous piecewise function
If you try to merge them … you no longer have a function
It fails the vertical line test!

5. An Absolute Value function is a famous piecewise function
If you try to merge them … you no longer have a function
Unless, of course, you restrict the domain of each portion.

6. An Absolute Value function is a famous piecewise function

7. Piecewise Functions
Functions are not always made up of a single equation. They can be made up of several pieces (if the domain is restricted properly).
The Absolute Value Function This piecewise function is made up of three pieces.
is made up of two pieces.
Evaluate the function for the following values of x.
1. x = 0
2. x = 1
3. x = 5
4. x = -2
5. x = 2
6. x = 10

8. f( ) = f( ) = f( ) = Graph Piecewise Functions
Graph the following. Make sure you look at the restricted domain.
Tell whether or not it is a function. Evaluate for the specific given values.
Function? Yes or No Function? Yes or No Function? Yes or No
f( ) = f( ) = f( ) =

9. Write Piecewise Functions
Write a piecewise function for the following graphs. Make sure you write the restricted domain next to each piece.
Then evaluate the function for the given values.

10. STEP FUNCTIONS GREATEST INTEGER FUNCTIONS.
There are special piecewise function called
STEP FUNCTIONS
and
GREATEST INTEGER FUNCTIONS.

11. A step function is a piecewise function consisting only
of horizontal lines, or constants.

12. The greatest integer function, written as
is a step function that yields the greatest integer
that is not larger than x.

13. Greatest Integer Function
For all real numbers, x, the greatest integer function returns the largest integer LESS THAN OR EQUAL TO x.
In other words, the greatest integer function rounds DOWN a real number to the nearest integer.
You can think of the solution as the “greatest integer” up to that point.
Evaluate the greatest integer function for the following values of x.
1. x = 4
2. x = 1.2
3. x = 6.1
4. x = 6.9
5. x = 103.5
6. x = -1.5
7. x = -4.8
8. x = -10.2

14. Extra
examples of
Piecewise Functions

16. You can evaluate a piecewise function
You have to pay particularly close attention to the domain so that you know which portion of the equation to plug your value into.

17. See if you can write the equations for the piecewise function g(x), restricting the domain appropriately.
Note: there are three pieces

18. See if you can write the equations for the piecewise function f(x), restricting the domain appropriately.
Note: there are three pieces