Teacher Resource
Algebra II Common Core, Unit 4
Building Polynomial Functions: Addition, Subtraction, Composition
Discussion facilitation suggestions:
1. What is the scenario describing? What is the important information in the scenario?
What mathematical operations apply? How would you create a function to represent the
scenario? Can you explain why you chose your method?
2. Follow-up: What do you notice about the new function? What are some
similarities/differences between the new function and the functions that were used to
create them? What happens when two functions are added, subtracted, or composed?
How does it come through in the new function?
Scenario 1:
Smyth Jewelers is designing a custom engagement ring for a customer. The weight of an ideal
round-cut diamond can be modeled by f (d)  0.0072d 3  0.093d 2  0.38d , where f (d) is the
diamond’s weight, in carats, and d is its diameter, in millimeters. The customer would like three
diamonds of the same weight on the engagement ring. Write a function to represent the total
weight, in carats, of the diamonds.
Scenario 2:
Smyth Jewelers’ charges can be modeled by g(x)  3990x , where g(x) represents the cost of
the diamond’s weight and x represents the diamond’s weight. The weight of the diamonds on the
engagement ring is modeled by f (d)  0.0144d 3  0.086d 2  0.27d , where f (d) represents the
diamond’s weight, in carats, and d is the diameter of the diamond, in millimeters. Write a
function to represent the total cost of diamonds on the engagement ring the customer designed.
Scenario 3:
The customer has decided to make some changes to the design of the engagement ring. The new
design consists of one diamond with the original diameter and two diamonds with a diameter 2
millimeters less. The weight of an ideal round-cut diamond can be modeled by
f (d)  0.0072d 3  0.093d 2  0.38d , where f (d) is the diamond’s weight, in carats, and d is its
diameter, in millimeters. Write a function to represent the new total weight of the diamonds, in
carats.
Scenario 4:
The latest design for the engagement ring has a total weight that can be modeled by
h(d)  0.0376d 3  0.71d 2  0.145d , where h(d) represents the diamond’s weight, in carats, and
d is its diameter, in millimeters.
The customer has decided to make some last minute changes to the design. The ring designers at
Smyth have been instructed to remove the diamond halo around the center diamond. The
diamond halo has a weight that can be modeled by p(d)  0.0193d 3  0.39d 2  0.27d , where
p(d) represents the weight, in carats, of the diamonds in the halo and d is the diamond’s
diameter. Write a function to represent the new total weight of the diamonds, in carats.