1. Greatest Integer Function (Step Function)

2. The greatest integer of a real number x is represented by [x] and
Definition
The greatest integer of a real number x is represented by [x] and {

3. Examples [4.7] = 4 [17] = 17 [-5.1] = -6 [0.9] =
Round down to nearest integer
[-5.1] = -6
[0.9] =

4. Basic Greatest Integer Function

5. Example
The cost of parking is free for less than an hour and $1 per hour thereafter.
f(x)=[x]

6. Standard Equation Where each step in the graph has a length of
and a height of

7. Parameters A & B
Parameter A: Changes steps in a vertical stretch or contraction
Parameter B: Changes steps in a horizontal stretch or contraction

8. Parameters A & B
If b > 0, the steps are closed on the left and open on the right
If b < 0, the steps are open on the left and closed on the right

9. Parameters A & B If ab > 0, the function is increasing
If ab < 0, the function is decreasing

10. Four Cases ④ a < 0, b < 0 ① a > 0, b > 0

11. f(x) has zeros if and only if k is a multiple of a Ex.

12. Zeros
Since
Then solve

13. Zeros

14. Domain: Range: Initial value: Sign:
Other Properties
Domain:
Range:
Initial value:
Sign:
Graph the function and determine
when

15. Graph and find all properties of
Example
Graph and find all properties of

16. Example
Step Length:
Step height:

17. Example
Zeros:

18. Example
Init Value:
Domain:
Range:

19. Example

20. Homework
Workbook
P. 123 #1
P. 124 #4
P. 126 #10, 11 &12