Evaluating Costs and Ranges in Real-World Functions

1. A car rental company charges a base fee of $30 plus $0.20 per mile driven. Write a function to represent the total cost, C(m), of renting a car for m miles. What is the domain of this function?

• m >= 0

• m <= 100

• m = 0

• m < 0

2. Using the function from question 1, evaluate C(50). What is the total cost for driving 50 miles?

• $15.00

• $30.00

• $25.00

• $40.00

3. A local gym charges a monthly membership fee of $40 plus $5 for each class attended. Define the function M(c) for the total monthly cost based on the number of classes c. What is the range of this function if a member attends between 0 and 10 classes?

• [30, 80]

• [40, 100]

• [0, 50]

• [40, 90]

4. Evaluate M(7) using the function from question 3. What is the total cost for attending 7 classes?

• Total cost for attending 7 classes is $70.

• Total cost for attending 7 classes is $100.

• Total cost for attending 7 classes is $140.

• Total cost for attending 7 classes is $210.

5. A delivery service charges a flat fee of $15 plus $2 for each package delivered. Write the function D(p) for the total delivery cost based on the number of packages p. What is the domain of this function?

• D(p) = 15 + 2p; Domain: p < 0, p ∈ Z

• D(p) = 15 + 2p; Domain: p >= 0, p ∈ Z+

• D(p) = 10 + 3p; Domain: p > 0, p ∈ Z

• D(p) = 20 + p; Domain: p >= 0, p ∈ R

6. If a customer wants to deliver 10 packages, evaluate D(10). What will be the total delivery cost?

• $30

• $70

• $100

• $50

7. A school is organizing a field trip and charges $25 per student. Write a function S(n) to represent the total cost for n students. What is the range of this function if the number of students is between 1 and 50?

• [25, 1250]

• [0, 1000]

• [50, 1500]

• [25, 500]

9. A phone plan costs $50 per month plus $0.10 per text message sent. Define the function P(t) for the total monthly cost based on the number of text messages t. What is the domain of this function?

• t >= 0, where t is a non-negative integer

• t < 0, where t is a negative integer

• t is a positive integer only

• t is any real number

10. If a user sends 200 text messages, evaluate P(200). What will be the total monthly cost?

• $25.00

• $20.00

• $15.00

• $30.00