Algebra 2
Modeling With Function Composition HW
Name:
Period:
1. A company estimates that its cost and revenue can be modeled by the functions
𝐶(𝑥) = 0.75𝑥 + 20,000
where x is the number of units produced.
𝑅(𝑥) = 1.50𝑥
a. What is the cost to the company if 1 million units are produced?
b. What is the revenue to the company is 1 million units are sold?
c. If Profit is defined as the money left over from sales after all costs are taken
out, write a composite function to find P(x) using correct function notation.
d. Find the profit to the company if 1 million units are produced and sold.
Explain why your answer is reasonable.
2. Going to college can be expensive, so you are looking for the best deals. You have a
coupon to RC Willey for $100 off the price of a sofa. When you arrive at the store,
you find that the sofas are on sale for 25% off.
a. Use function notation to describe your cost using the coupon only.
b. Use function notation to describe your cost using only the 25% discount.
c. Write a composite function that describes your cost if you use the $100
coupon first, then take the 25% discount.
d. Write a composite function that describes your cost if you use the 25%
discount first, then use your $100 coupon.
e. Assume you found a sofa that you really like for $550.
i. What is the cost if only using your coupon? Use your function notation
to show your work.
ii. What is the cost if only using the 25% store discount? Use your
function notation to show your work.
iii. What is the cost if you use the $100 coupon first, then use the 25%
store discount? Use your function notation to show your work.
iv. What is the cost if you use the 25% discount first, then use the $100
coupon? Use your function notation to show your work.
f. Would you pay less for the sofa if you use the coupon first or took the 25%
discount first?