Question

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. 
 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)

Answer 1

a) How much would it cost to ship a package weighing 3.2 pounds? Explain how you arrived at your answer. 
Answer:
Shipping cost of 3.2 package is $4.13.
We can't use the cost assigned to 3 lbs because the package is over 3 lbs but it is not over 4 lbs so we use the cost of 4lbs. (check the attachment for price)

b)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.
Answer:
Line graph is needed to represent the Media Mail shipping prices as a function of the weight of the books shipped.
In line graph, x values represent the weight in pounds and the y values represent the cost.

c)Graph the Media Mail shipping prices as a function of the weight of the books shipped.
Answer;
When we graph the Media Mail shipping prices as a function of the weight of the books shipped, it will be;

f(x) = 2.69 + 0.48(x-1)

Answer 2

Using the information in the table given, the data models the relationship between weight and shipping cost. Hence ;

• 3.2 pounds will cost $4.13
• A scatter plot with a trend line
• Graph is attached below.

The cost of shipping a package which weighs 3.2 pounds will be the cost of packages in the 4 pounds category as it has exceeded the maximum weight for the 3 pounds class. Hence, the cost will be $4.13.

Graphing an independent and dependent variable is can be represented using a scatter plot with each pair of weight and shipping cost denoted by a mark on the graph.

Therefore, the graph of the relationship between weight and shipping cost is attached.

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