Real World Functions

Composition of Functions - Real Life

Application of Composition of Functions

Example #1

(Write this example down in your notes)

• You receive a $5.00 off a pair of jeans coupon in the mail.

• When you arrive at the store, you find that all jeans are 25% off.

• Let x represent the original cost of the jeans.

1. Write a function f(x) that represents the effect of your original coupon in the mail.

**Try to write function first BEFORE watching video**

1. Write a function g(x) that represents the effect of the 25% discount at the store.

**Try to write function first BEFORE watching video**

Multiple Choice

Write the composition of functions that represents how much you would pay if you used the mail coupon FIRST, followed by applying the discount from the store. 

• $$\left(f\degree g\right)\left(x\right)$$  

• $$\left(g\degree f\right)\left(x\right)$$  

Video Explanation of Composition of Function

• You used the mail coupon FIRST, followed by applying the discount from the store. 

• you applied the discount from the store 2nd. 

Multiple Choice

Simplify the function  $$\left(g\degree f\right)\left(x\right),$$ that represents how much you would pay if you used the mail coupon FIRST, followed by applying the store discount.

• $$\left(f\degree g\right)\left(x\right)=.75x-5$$   

• $$\left(f\degree g\right)\left(x\right)=.75x-3.75$$  
  

• $$\left(g\degree f\right)\left(x\right)=.75x-5$$  

• $$\left(g\degree f\right)\left(x\right)=.75x-3.75$$  

Multiple Choice

Write the composition of functions that represents how much you would pay if you used the store discount FIRST, followed by applying the coupon from the mail.

• $$\left(f\degree g\right)\left(x\right)$$  

• $$\left(g\degree f\right)\left(x\right)$$  

Video Explanation of Composition of Function

• You apply the discount from the store FIRST. 

• You used the mail coupon 2nd.

Multiple Choice

Simplify the function  $$\left(f\degree g\right)\left(x\right),$$ that represents how much you would pay if you used the store discount FIRST, followed by applying the coupon from the mail.

• $$\left(f\degree g\right)\left(x\right)=.75x-5$$   

• $$\left(f\degree g\right)\left(x\right)=.75x-3.75$$  
  

• $$\left(g\degree f\right)\left(x\right)=.75x-5$$  

• $$\left(g\degree f\right)\left(x\right)=.75x-3.75$$  

Multiple Choice

You found a pair of jeans for $36 originally. How much would you pay if you used the mail coupon first followed by the store discount (assuming no sales tax)?

• $23.75

• $27.00

• $22.00

• 25.50

Multiple Choice

You found a pair of jeans for $36 originally. How much would you pay if you used the store discount first followed by the coupon from the mail (assuming no sales tax)?

• $23.75

• $27.00

• $22.00

• 25.50

Multiple Choice

Which composition of functions will give you the better deal on the $36 jeans?

• Use coupon from mail first and then use store discount.

• Use store discount first and then use coupon from the mail.

• The order you use the coupon and store discount do not matter.

Multiple Choice

Which composition of functions will give you the better deal on the $36 jeans?

• Use coupon from mail first and then use store discount.

• Use store discount first and then use coupon from the mail.

• The order you use the coupon and store discount do not matter.

If you only have $40 with you, what's the most expensive pair of jeans you can purchase?

(Assuming no sales tax.)

Multiple Choice

Calculate 1st part:

If you only have $40 with you, what's the most expensive pair of jeans you can purchase if you use coupon from mail first, followed by discount from store?

• $25.00

• $26.25

• $60.00

• $58.33

Multiple Choice

Calculate 2nd part:

If you only have $40 with you, what's the most expensive pair of jeans you can purchase if you use store discount first, followed by coupon from mail?

• $25.00

• $26.25

• $60.00

• $58.33

Graph both functions f(g(x)) and g(f(x)) in your calculator at the same time.

Multiple Choice

Looking at the graphs in your calculator, will the 2 graphs ever intersect?

• Yes

• No

Explanation of graphs in your calculator, will the 2 graphs ever intersect?

• f(g(x))=.75x-5

• g(f(x))=.75x-3.75

Multiple Choice

Is there a "break even" point on the graph, where both methods would cost the same?

• Yes.

• No.

Multiple Choice

Which composition of functions will give you the better deal on jeans at this store?

• Use coupon from mail first and then use store discount.

• Use store discount first and then use coupon from the mail.

• The order you use the coupon and store discount do not matter.