Exploring Domain and Range of Real-World Functions

1. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a function to represent the total cost, C, as a function of miles driven, m. What is the domain of this function?

• m >= 0

• m = 50

• m < 0

• m <= 100

2. A local gym charges a monthly membership fee of $30 and an additional $5 for each class attended. Define a function for the total cost, T, based on the number of classes, c. What is the range of this function if a member attends between 0 and 10 classes?

• [0, 50]

• [30, 100]

• [30, 80]

• [35, 75]

3. A farmer sells apples for $2 each. If the number of apples sold is represented by the function A(x) = 2x, where x is the number of apples, what is the domain of this function?

• x >= 0, x ∈ R

• x >= 0, x ∈ Z+

• x < 0, x ∈ Z+

• x > 0, x ∈ Z

4. A movie theater has a ticket price that varies based on age: $10 for adults and $5 for children. Define a piecewise function, P(a), for the price based on age, a. What is the domain of this function?

• (0, 18)

• [5, 10]

• (-∞, 0)

• [0, ∞)

5. A delivery service charges a base fee of $15 plus $1.50 per mile. Write a function for the total delivery cost, D, based on the distance in miles, d. What is the domain of this function?

• d = 0

• d >= 0

• d < 0

• d <= 10

6. A school is planning a field trip and charges $25 per student. If the number of students is represented by the function S(n) = 25n, where n is the number of students, what is the domain of this function?

• n < 0, n ∈ Z

• n >= 0, n ∈ Z+

• n = 25, n ∈ Z+

• n > 0, n ∈ R

7. A subscription service charges $10 per month plus $2 for each additional movie rented. Write a function for the total cost, C(m), based on the number of movies rented, m. What is the range of this function if a customer rents between 0 and 5 movies?

• $10, $12, $14, $16, $18, $22

• [10, 12, 14, 16, 18, 20]

• $8, $10, $12, $14, $16

• $10, $11, $13, $15, $17

8. A local bakery sells cupcakes for $3 each. If the number of cupcakes sold is represented by the function C(x) = 3x, where x is the number of cupcakes, what is the domain of this function?

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

• x is a negative integer

• x is any real number

• x < 0

9. A taxi service charges a flat rate of $3 plus $2 per mile. Define a function for the total fare, F(m), based on the miles traveled, m. What is the domain of this function?

• m >= 0

• m < 0

• m <= 10

• m = 0

10. A concert venue has ticket prices that vary: $50 for general admission and $75 for VIP. Define a piecewise function, T(a), for the ticket price based on the type of admission, a. What is the domain of this function?

• $25 for VIP

• $100 for general admission

• {'general admission', 'VIP'}

• $50 and $75