Warm Up What is an integer? Determine the largest integer that “fits” into the following values: 4.55 6.01 7.99 Challenge: - 3.5

Answers What is an integer? The set of positive and negative natural numbers. Determine the largest integer that “fits” into the following values: 4.55 4 6.01 6 7.99 7 Challenge: - 3.5 -4

Greatest Integer Functions

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!

Greatest Integer Functions How does it work? any number integer

Use the following equations to make a statement about what the greatest integer machine does to a number. 3.15 3 -17.2 -18 18.99 18 -6.99 -7 -8.5 -9 101.25 101

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.

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.

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

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.