Mastering Domain and Range Through Real-World Problems

1. A local park has a rectangular playground that is 30 meters long and 20 meters wide. If the playground is represented by the function f(x) = 20, what is the domain and range of this function?

• Domain: [0, 30], Range: {20}

• Domain: [0, 30], Range: {0, 30}

• Domain: [0, 30], Range: {0, 20}

• Domain: [0, 20], Range: {20}

2. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If the total cost is represented by the function C(m) = 50 + 0.2m, what is the domain of this function in terms of miles driven?

• [-10, 100]

• (0, 100)

• [0, 100]

• [0, ∞)

3. A swimming pool can hold a maximum of 5000 liters of water. If the water level is represented by the function h(t) = 5000 - 100t, where t is time in hours, what is the range of this function?

• [0, 500]

• [0, 5000]

• [0, 10000]

• [100, 5000]

4. A farmer grows two types of crops: corn and wheat. The amount of corn produced can be modeled by the function C(x) = 100 - 2x, where x is the number of acres planted. What is the domain of this function?

• [0, 25]

• [0, 100]

• [-10, 50]

• [0, 50]

5. A concert venue has a seating capacity of 2000 people. If the number of tickets sold is represented by the function T(x) = 2000 - x, where x is the number of tickets sold, what is the range of this function?

• [0, 200]

• [1000, 2000]

• [0, 2000]

• [0, 1000]

6. A delivery truck can carry a maximum weight of 3000 kg. If the weight of the cargo is represented by the function W(x) = 3000 - 50x, where x is the number of boxes, what is the domain of this function?

• [0, 50]

• [0, 100]

• [0, 75]

• [0, 60]

7. A bicycle rental shop charges $15 for the first hour and $5 for each additional hour. If the total cost is represented by the function C(h) = 15 + 5(h - 1) for h > 1, what is the domain of this function?

• [1, 5]

• (1, ∞)

• (0, 1)

• (1, 10)

8. A water tank can fill at a rate of 200 liters per hour. If the amount of water in the tank is represented by the function W(t) = 200t, what is the range of this function after 5 hours?

• [0, 500]

• [0, 2000]

• [100, 1000]

• [0, 1000]

9. A school is planning a field trip and can take a maximum of 120 students. If the number of students attending is represented by the function S(x) = 120 - x, where x is the number of students who opt out, what is the domain of this function?

• [-10, 120]

• [0, 130]

• [0, 120]

• (0, 120)

10. A bakery sells cupcakes for $3 each. If the total revenue is represented by the function R(x) = 3x, where x is the number of cupcakes sold, what is the range of this function if they sell between 0 and 100 cupcakes?

• [0, 100]

• [0, 300]

• [0, 150]

• [0, 500]