Answer the following questions in order to get a better understanding of how to do your
project. (Optional)
You are selling candy bars. The taxable amounts and tax imposed up to $1 are shown below.
• For amounts between $0.01 and $0.20, the tax is $.01.
• For amounts greater than $0.20 and less than or equal to $0.40, the tax is $0.02.
• For amounts greater than $0.40 and less than or equal to $0.60, the tax is $0.03.
• For amounts greater than $0.60 and less than or equal to $0.80, the tax is $0.04
• For amounts greater than $0.80 and less than or equal to $1.00, the tax is $0.05.
1) Complete the graph to show the tax imposed on the candy bars.
Use the graph to answer the following questions:
2) A candy bar costs $0.55. What is the total cost with tax?
3) Your aunt purchased three candy bars at $0.55 a piece. What is the total cost with tax?
4) Someone purchased 4 candy bars at $0.55 a piece. They gave you $2 and a quarter. Is this
enough money to cover the candy bars and the tax? Explain your answer.
Suppose a long-distance phone company calculates their charges so that a call of exactly 3 minutes will cost the same as
a call of 3.25 min or 3 .9 min, and there is no increase in cost until you have been connected for 4 min. Increases are
calculated after each additional minute. We call this the greatest integer function, which outputs the greatest integer
less than or equal to x. Because the graph of this function looks like a staircase, it is called a step function.
a.
Use the greatest integer function to write cost equations for two long distance phone companies below. “20
cents for the first minute of a phone call and 17 cents for each minute after that, and 50 cents for the first
minute and 11 cents for each additional minute.”
b. Graph the two new equations representing the two companies.
c. Now determine when each plan is more desirable. Explain your reasoning.
Unit 2 Project: Step Functions in the Real World
Overview:
The graph represents a step function. The open circles mean that those points are not included in the graph. For
example, the value of f(3) is 5, not 2. The places where the graph “jumps” are called discontinuities.
One function we often use is something called the greatest integer function, f(x) = [x]
Instructions:
Do further research on the



greatest integer function
ceiling function
floor function.
Prepare a report on the functions. Your project should include



A graph of each function, completed by hand, with labels, scales, etc.
A written or verbal description, in your own words, of how each function operates, including any relationships
among the three functions. Be sure to explain how you would evaluate each function for different values of x.
Examples of how each function might be applied in a real-world situation.
As you do your research, you might learn about other step functions that you’d like to include in your project. (Extra
credit)
Grading
This will be a 50 point formative or summative assessment of your choice.
You must choose before I grade it.
Use the following rubric as a guide as to how you will be graded.
Name: ____________________________________________
Due: October 29th or October 30th
Chapter 2 Project – Step Functions
Rubric for grading
I want this project to be a (circle one):
50 point summative
Category
Greatest
Integer
Function
Ceiling
Function
Floor
Function
or
100 point formative
Possible Points
Graph
3
Description
2
How to evaluate the function for
different values of x.
Example applied in a real-world
situation
2
3
Graph
3
Description
2
How to evaluate the function for
different values of x.
Example applied in a real-world
situation
2
3
Graph
3
Description
2
How to evaluate the function for
different values of x.
Example applied in a real-world
situation
Written Relationship between the three
functions
2
3
5
Neatness and Organization
10
Hand in on time
5
Extra Credit
10 per function
Total
50
Points Earned