Successive Discounts
NAME ___________________________
Composition of functions involves applying two or more functions in succession.
One of the places that this topic occurs is in retail stores, when successive discounts are taken.
Using this context, you will examine composition of functions.
In the mail, you receive a coupon for $5 off of a pair of jeans. When you arrive at the store, you
find that all jeans are 25% off. You find a pair of jeans for $36.
1.
If you use the $5 off coupon first, and then you use the 25% off on the remaining amount,
how much will the jeans cost?
2.
If you use the 25% off first, and then you use the $5 off on the remaining amount, how
much will the jeans cost? How will the situation change for jeans that cost more or less
than $36?
How will the situation change for jeans that cost more or less than $36?
3.
Let the cost of the jeans be represented by a variable x. Write a function f(x) that
represents the cost of the jeans after the $5 off coupon.
4.
Write a function g(x) that represents the cost of the jeans after the 25% discount.
5.
Write a new function r(x) that represents the cost of the jeans if the 25% discount is
applied first and the $5 off coupon is applied second.
6.
Write a new function s(x) that represents the cost of the jeans if the $5 off coupon is
applied first and the 25% discount is applied second.
Successive Discounts
7)
NAME ___________________________
A store is offering a 15% discount on all items. You have a coupon worth $2 off any item. Let x
be the original cost of an item. Use a composition of functions to find a function
that gives
the final cost of an item if the discount is applied first and then the coupon. Then use this
function to find the final cost of an item originally priced at $10.
8) A boutique prices merchandise by adding 80% to its cost. It later decreases by 25% the price of
items that don’t sell quickly.
a) Write a function
to represent the price after 80% markup.
b) Write a function
to represent the price after the 25% markdown.
c) Use a composition function to find the price of an item after both price adjustments that
originally costs the boutique $150.
d) Does the order in which the adjustments are applied make a difference? Explain.
9) Use
,
and
. Compare the boxed quantity in Column A with the
boxed quantity in Column B. Choose the best answer.
A.
B.
C.
D.
The quantity in Column A is greater.
The quantity in Column B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
A
1
2
B