Evaluating and Graphing Composite Functions in Real-Life Scenarios

1. A car rental company charges a base fee of $30 plus $0.20 per mile driven. If the total cost function is C(m) = 30 + 0.2m, and a customer drives d miles, express the total cost as a composite function C(d) = C(m(d)). Evaluate C(100) to find the total cost for driving 100 miles.

• 50

• 70

• 90

• 110

2. A bakery sells cupcakes for $2 each and charges a delivery fee of $5. If the function for the number of cupcakes ordered is N(x) = x, and the total cost function is T(N) = 2N + 5, find the composite function T(N(x)). What is the total cost for ordering 12 cupcakes?

• 25

• 29

• 32

• 20

3. A fitness center charges a monthly membership fee of $50 and an additional $10 for each class attended. If the function for the number of classes attended is C(x) = x, express the total cost as a composite function T(C(x)). Evaluate T(C(5)) to find the total cost for attending 5 classes in a month.

• 90

• 75

• 110

• 100

4. A phone plan charges a flat rate of $40 plus $0.10 per text message sent. If the function for the number of text messages sent is T(x) = x, express the total cost as a composite function C(T(x)). Graph the function for 0 to 100 text messages and identify the slope.

• C(x) = 40 + 0.05x; slope = 0.05

• C(x) = 40 + 0.20x; slope = 0.20

• C(x) = 30 + 0.10x; slope = 0.10

• C(x) = 40 + 0.10x; slope = 0.10

5. A gardener charges a flat fee of $25 for a consultation and $15 per hour of work. If the function for hours worked is H(x) = x, express the total cost as a composite function C(H(x)). Evaluate C(H(3)) to find the total cost for 3 hours of work.

• 85

• 50

• 100

• 70

6. A streaming service charges $10 per month and an additional $2 for each movie rented. If the function for the number of movies rented is M(x) = x, express the total cost as a composite function C(M(x)). What is the total cost for renting 4 movies?

• 18

• 22

• 20

• 15

7. A delivery service charges a base fee of $15 plus $0.50 per mile. If the function for the distance in miles is D(x) = x, express the total cost as a composite function C(D(x)). Evaluate C(D(10)) to find the total cost for a 10-mile delivery.

• 20

• $30

• $25

• $15

8. A school charges a registration fee of $100 and $20 per class. If the function for the number of classes taken is C(x) = x, express the total cost as a composite function T(C(x)). Evaluate T(C(6)) to find the total cost for taking 6 classes.

• 220

• 250

• 300

• 180

9. A subscription box service charges $25 per box and $5 for shipping. If the function for the number of boxes ordered is B(x) = x, express the total cost as a composite function C(B(x)). What is the total cost for ordering 3 boxes?

• $100

• $70

• $90

• $80

10. A gym charges a $40 initiation fee and $30 per month. If the function for the number of months is M(x) = x, express the total cost as a composite function C(M(x)). Evaluate C(M(6)) to find the total cost for a 6-month membership.

• 300

• 180

• 220

• 250