1. Graphing Step (Greatest Integer) Functions
Unit 4 Day 4
Graphing Step (Greatest Integer) Functions

2. Warm Up 1. Why does the inverse variation have a vertical asymptote?
Graph:
a b.

3. Warm Up 1. Why does the inverse variation have a vertical asymptote?
Graph:
a b.

4. Homework Answers Packet p.5 odd
1) 3)
5) 7)
9) )
HA: y = HA: y = -3
VA: x = VA: x = -3

5. Homework Answers Packet p.5 odds
13) )
HA: y = HA: y = 1
VA: x = VA: x = 2
17) Let x = dependent variable = # of awards
Let a = # of awards, c = cost of awards
H.A. c = 0 (like y = 0) V.A. a = 0 (like x = 0)
Theoretical Domain: a < 0, a > 0 Practical Domain: a > 0
Theoretical Range: c < 0, c > 0 Practical Domain: c > 0
As the school buys more awards, they have less money to spend on each award so c = 0 (y = 0), the horizontal asymptote.
As the school buys less awards, they have more money to spend on each award so a = 0 (x = 0), the vertical asymptote.

6. Homework
Packet p. 6 and 7

7. Notes: Graphing Step (Greatest Integer) Functions
Definition
The domain is the set of possible x-values.
The output of a function is called the range.
Problem 1 – Cell Phone Situation
Your friend got a cell phone that charges 40 cents per minute or part thereof. However, he is not allowed to use it for more than 4 minutes.
What was the fee if he talked for
22 seconds:
45 seconds:
62 seconds:
180 seconds:
If the cost is a function of time, what is the domain of the cost function (in seconds)?

9. Greatest Integer Discovery
On Calc
Notes p (top ½)

10. Summary
This type of function is called a greatest integer function. On the graphing calculator, graph y = int(x). Be sure to note where the open circles and closed circles are.
We’ll come back and graph in a minute…let’s learn to evaluate 1st!
The piecewise function at right is defined symbolically as and verbally as “the greatest integer less than or equal to x” or, in other words, kind of like a “round down” function OR like the show “Price is Right”.
It is a step function, and the graph is said to have “jump discontinuities” at the integers.

11. Evaluating with Greatest Integer Function
The piecewise function at right is defined symbolically as and verbally as “the greatest integer less than or equal to x” or, in other words, kind of like a “round down” function OR like the show “Price is Right”. It is a step function, and the graph is said to have “jump discontinuities” at the integers.
Drawing a number line can help…especially with negative values!
Evaluate the following:
(3) = (4) = (5) =
You Try!
(6) = (7) = (8) =
You Try! You Try! 1 3 7 -7 -3

12. Solving with Greatest Integer Function
The piecewise function at right is defined symbolically as and verbally as “the greatest integer less than or equal to x” or, in other words, kind of like a “round down” function OR like the show “Price is Right”. It is a step function, and the graph is said to have “jump discontinuities” at the integers.
Each solution will be a set of values, not just 1 number!
Solve the following equations for x and write the answers in set notation:
9) )

13. Now, let’s graph!
On the graphing calculator, graph y = int(x). Be sure to note where the open circles and closed circles are. It is the greatest integer less than or equal to x” .

14. Graphing Greatest Integer Function Translations
Practice
Notes p. 14
Graphing Greatest Integer Function Translations

15. Notes p. 12

16. Notes p. 12

17. Notes p. 12

18. Summary
and if

19. Graphing Greatest Integer Functions
Practice
Notes p. 13
Graphing Greatest Integer Functions

22. Practice p. 13

23. Homework
Packet p. 6 and 7