Understanding Domain and Range in Real-World Functions

1. A function f(x) = 2x + 3 represents the cost in dollars of x items purchased. What is the domain of this function if x must be a whole number?

• x ∈ {0, 1, 2, ...}

• x ∈ {1, 2, 3, ...}

• x ∈ {-1, 0, 1, 2, ...}

• x ∈ {0, 0.5, 1, ...}

2. The function g(t) = -5t + 20 models the height in meters of a ball thrown upwards after t seconds. What is the range of this function if the ball is thrown from a height of 20 meters?

• [5, 20]

• [0, 5]

• [0, 20]

• [0, 15]

3. A car rental company charges a flat fee of $50 plus $0.20 per mile driven, represented by the function C(m) = 50 + 0.2m. What is the domain of this function in the context of miles driven?

• m < 0

• m <= 100

• m = 50

• m >= 0

4. The function h(n) = 3n - 1 describes the number of books a student can read in n weeks. If the student can read a maximum of 10 books, what is the range of this function?

• [1, 2, 3, 4]

• [-1, 2, 5, 8]

• [0, 4, 7, 10]

• [-1, 3, 6, 9]

5. A swimming pool can hold a maximum of 5000 liters of water. The function V(d) = 5000 - 100d represents the volume of water left after d days of evaporation. What is the domain of this function?

• [0, 50]

• [0, 25]

• [0, 100]

• [0, 75]

6. The function p(x) = x^2 models the area of a square garden in square meters as a function of the length of one side x. What is the domain of this function if x must be a positive number?

• [0, ∞)

• [0, 10]

• (-∞, 0)

• (0, ∞)

7. A delivery service charges a base fee of $15 plus $1.50 per mile. The cost function is C(d) = 15 + 1.5d. What is the range of this function if the maximum distance for delivery is 30 miles?

• [0, 30]

• [15, 60]

• [10, 50]

• [15, 45]

8. The function r(t) = 4t + 10 represents the total revenue in dollars from selling t tickets to a concert. If the maximum number of tickets sold is 200, what is the range of this function?

• [10, 600]

• [10, 1000]

• [10, 810]

• [0, 800]

9. A plant grows according to the function G(d) = 2d + 5, where d is the number of days. If the plant can grow a maximum of 50 cm, what is the domain of this function?

• [0, 22]

• [0, 50]

• [0, 10]

• [5, 15]

10. The function S(x) = 10 - x models the number of students remaining in a classroom after x students leave. If no more than 10 students can leave, what is the range of this function?

• [0, 5]

• [5, 10]

• [0, 10]

• [-5, 10]