1. Warm Up
What is an integer? Determine the largest integer that “fits” into the following values: Challenge: - 3.5

2. Answers
What is an integer? The set of positive and negative natural numbers. Determine the largest integer that “fits” into the following values: Challenge:

3. Greatest Integer Functions

5. Greatest Integer Functions
Greatest integer functions use the following notation:
any number
integer
This is the greatest integer machine! Put a number in, get an integer out!

6. Greatest Integer Functions
How does it work?
any number
integer

7. Use the following equations to make a statement about what the greatest integer machine does to a number.

8. 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 -7
When you use the greatest integer function, the answer is the integer on the immediate left on the number line.
Exception: When you evaluate an exact integer, like 3, the answer is the integer itself.

9. When all these points are strung together the graph looks something like a series of steps.
Notice that the left of each step begins with a closed point, but the right of each step ends with an open point.

10. Rather than place a long series of points on the graph, a line segment can be drawn for each step.

11. The graphs shown thus far have been magnified to make a point
The graphs shown thus far have been magnified to make a point. However, these graphs are usually shown at a normal scale.