Book Sales Online book sales continue to increase in popularity because it is convenient and customers can find books that are not available in their local bookstores. Today, you will investigate several aspects of the book business using nonlinear functions.

Directions
Complete each of the following tasks, reading the directions carefully as you go. Be sure to show all work where indicated, including inserting images of graphs. Be sure that all graphs or screenshots include appropriate information such as titles, labeled axes, etc. If your word processing program has an equation editor, you can insert your equations here. Otherwise, print this activity sheet and write your answers by hand.
In addition to the answers you determine, you will be graded based on the work you show, or your solution process. So, be sure to show all your work and answer each question as you complete the task. Type all your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.
Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy.
Now, let’s get started!

Part 1: Graph piecewise functions from tables and equations.
Isabel sells new and used mystery novels online. Her customers are primarily in the United States. She sends up to 10 pounds of books in one shipment. She uses the United States Postal Service’s Media Mail service because it is inexpensive for her customers. Current Media Mail shipping prices for book shipments weighing 10 pounds or less appear below.

Weight Not Over (lbs.)
Price
0
$0
1
$2.69
2
$3.17
3
$3.65
4
$4.13
5
$4.61
6
$5.09
7
$5.57
8
$6.03
9
$6.49
10
$6.95

How much would it cost to ship a package weighing 3.2 pounds? Explain how you arrived at your answer. (3 points)

What type of graph is needed to represent the Media Mail shipping prices as a function of the weight of the books shipped? Explain your thinking. (3 points)

Graph the Media Mail shipping prices as a function of the weight of the books shipped. (10 points)

What is the domain and range of the graphed function? (3 points)

Isabel’s competition, who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. (5 points)

Graph the function in part e. (10 points)

Is your graph discrete or continuous? Explain. (5 points)

Part 2: Solve a real-world problem using a square root function.
When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.
The total length of each row of bookshelves will be 45 of the length of the storage space.
Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)

Write a function that expresses f(x). (10 points)

Graph the function. (10 points)

Part 3: Solve a real-world problem using a cube root function.
Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.
f(x) = 10003x + 1000
How many books were sold after 8 months? (3 points)

Graph the function. (10 points)

Part 4: Solve a real-world problem using an absolute value function.
A transaction is positive if there is a sale and negative when there is a return. Each time a customer uses a credit card for a transaction, the credit company charges Isabel. The credit company charges 1.5% of each sale and a fee of 0.5% for returns.
Let x represent the amount of a transaction and let f(x) represent the amount Isabel is charged for the transaction. Write a function that expresses f(x). (10 points)

Graph the function. (10 points)

What are the domain and range of the function? (5 points)