Composite Functions: Cost Calculations and Transformations

1. A car rental company charges a base fee of $30 plus $0.20 per mile driven. If a customer drives 'x' miles, write a function for the total cost, C(x). If the customer drives 50 miles, what is the total cost?

• $50

• $30

• $60

• $40

2. A gym charges a monthly membership fee of $40 and an additional $5 for each class attended. If a member attends 'y' classes, express the total cost as a function, G(y). If a member attends 8 classes, what is the total cost?

• $100

• $70

• $80

• $90

3. A factory produces 'x' items, and the profit from selling these items is given by the function P(x) = 50x - 200. If the factory produces 100 items, what is the profit?

• 4000

• 5000

• 6000

• 4800

4. A student scores 'x' points on a test, and the final grade is calculated using the function F(x) = 0.8x + 10. If the student scores 75 points, what is the final grade?

• 65

• 80

• 70

• 90

5. A delivery service charges a flat rate of $15 plus $2 for each package delivered. If a delivery person delivers 'n' packages, write the function D(n) for the total charge. What is the total charge for delivering 10 packages?

• 45

• 35

• 50

• 25

6. A store offers a discount of 20% on the total purchase price 'p'. Write the function for the discounted price, D(p). If a customer spends $150, what is the discounted price?

• $140

• $100

• $130

• $120

7. A phone plan charges a monthly fee of $25 plus $0.10 per text message sent. If a user sends 'm' messages, express the total cost as a function, T(m). What is the total cost if the user sends 200 messages?

• 45

• $30

• $50

• $75

8. A gardener charges $50 for the first hour and $30 for each additional hour. If the gardener works for 'h' hours, write the function G(h) for the total charge. What is the total charge for 4 hours of work?

• $100

• $160

• $120

• $140

9. A subscription service charges $10 per month plus a one-time setup fee of $20. If a customer subscribes for 'm' months, express the total cost as a function, S(m). What is the total cost for a 6-month subscription?

• $40

• $100

• $60

• $80

10. A restaurant bill includes a 15% tip on the total amount 'b'. Write the function for the total bill including tip, T(b). If the bill before tip is $80, what is the total bill including tip?

• 92

• 100

• 85

• 75