1. Warm Up #4 1.A) What is an integer? B) Give 3 examples of integers. 2. Given: a)What is the horizontal asymptote? b)What is the vertical asymptote? c)As x  -∞_________ As x  ∞________

2. Essential Question What are characteristics of the Greatest Integer Function?

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

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

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

7. 012345678-2-3-4-5-6-7 When you use the greatest integer function, the answer is the integer on the immediate left on the number line. 6.31-6.31 Exception: When you evaluate an exact integer, like 3, the answer is the integer itself. 3

8. xy 0.25.5.75 1 1.25 1.5 1.75 2 Graphing Greatest Integer Functions

9. xy 0.25.5.75 1 1.25 1.5 1.75 2 What if we kept going?

10. 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.

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

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

13. Just remember: Closed point on the left, open point on the right! Graphing Greatest Integer Functions in the Calculator You can use the “int( )” function in your calculator to graph greatest integer functions.

14. Example 4 Use your calculator to graph the following function:

15. Example 5: Wheels Bike Rentals charges a $6.00 flat rate and any time up until 1 hour. Then for each additional hour you are charged $1.50 to rent a bicycle including fractions of an hour. Use the greatest integer function to create a model for the cost C of renting a bicycle for x hours. Sketch the graph for up to 5 hours. xC

16. Example 5: Wheels Bike Rentals charges a $6.00 flat rate and $1.50 for each hour you rent a bicycle including fractions of an hour.Use the greatest integer function to create a model for the cost C of renting a bicycle for x hours. Sketch the graph for up to 5 hours.