Composition of Functions!A REAL WORLD EXAMPLE

Let’s face it! Most Americans enjoy a great pair of jeans. And buying them on sale seems like an awesome way to get more

bang for your buck!

In our application we will look at the effect of two different deductions and discounts, and determine which combination of

deductions is better for the consumer.

OUR ASSIGNMENT IS TO DETERMINE CARLTON’S COST TO PURCHASE A PAIR OF JEANS WHEN HE PURCHASES A $50 PAIR OF JEANS BY :a) USING ONLY THE STORE PROMOTION OF 20% OFFb) USING ONLY THE $15 CUSTOMER REWARD COUPONc) USING THE STORE PROMOTION OF 20% OFF AND THEN THE $15 COUPONd) USING THE $15 OFF COUPON AND THEN THE STORE PROMOTION OF 20%

A) WHAT WILL CARLTON’S COST BE TO PURCHASE A $50 PAIR OF JEANS IF HE USES ONLY THE 20% OFF STORE PROMOTION?

B) WHAT WILL CARLTON’S COST BE TO PURCHASE A $50 PAIR OF JEANS IF HE USES ONLY THE $15 OFF CUSTOMER LOYALTY COUPON?

$𝟓𝟎−$𝟏𝟓=$𝟑𝟓

C) WHAT WILL CARLTON’S COST BE TO PURCHASE A $50 PAIR OF JEANS IF HE USES THE 20% OFF STORE DISCOUNT AND THEN THE $15 COUPON?

ORIGINAL PRICE – 20% DISCOUNT – COUPON = COST

D) WHAT WILL CARLTON’S COST BE TO PURCHASE A $50 PAIR OF JEANS IF HE USES THE $15 COUPON AND THEN THE 20% OFF STORE DISCOUNT?

ORIGINAL PRICE – COUPON – 20% 0FF THE REDUCED PRICE = COST

It DOES matter the order that the discounts are applied.

How does this apply to what we will learn about composition of functions?

- Each discount is a function of the cost of the jeans. In one function we are reducing the cost by 20%. In the other function we are subtracting $15 from the cost. - When we use BOTH of these functions, the order that we apply them makes a difference in the answer.

Composition of Functions – The BASICS

This is a function of 20% off a price.This is a function of $15 off a price.

represents applying the 20% off discount first. Notice how the innermost function is the % off.

represents applying the coupon first and then the 20% reduction. Notice how the inner most function is the coupon.

Composition of Functions – The BASICS

This is a function of 20% off a price.This is a function of $15 off a price.