Algebra 2 6-6 Guided Practice: Function Operations

by Matthew Richardson

| 9 Questions1

10

Solve It! You want to buy a sofa that was marked down by $100 before the clearance discount was applied.

The furniture store may add the 5% sales tax before applying the additional discount, or it may add the sales tax after applying the additional discount. Which way is better for you, the customer?

Before

After

2

10

Solve It! In the above item, how much do you save by choosing the less expensive option?

Enter your response in this format: $12.30

3

3

10

Problem 1 Got It?

A

B

C

D

4

4

10

Problem 2 Got It?

A

B

C

5

5

10

Problem 3 Got It?

A

B

C

D

6

10

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 15% discount and then the 20% discount.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.85x and E(x) = 0.80x. (E ◦ D)(x) = 0.68x.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.80x and E(x) = 0.85x. (E ◦ D)(x) = 0.68x.

7

10

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 20% discount and then the 15% discount.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.85x and E(x) = 0.80x. (D ◦ E)(x) = 0.68x.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.80x and E(x) = 0.85x. (D ◦ E)(x) = 0.68x.

8

10

Problem 4 Got It? Reasoning: In the scenario above, which order of discounts results in a lower cost to the employee?

Taking the 15% discount first results in a lower price.

The total discounts are the same, so it does not matter which discount you take first.

Taking the 20% discount first results in a lower price.

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