1. **State the problem:** We are given the linear function $$W = 6F + 4000$$ where $W$ is the weight of the airplane and $F$ is the amount of fuel. 2. **Identify the domain:** The fuel amount $F$ ranges from 0 to 300 gallons, so the domain is $$0 \leq F \leq 300$$. 3. **Calculate the range:** Substitute the domain endpoints into the function: - When $F=0$, $$W = 6(0) + 4000 = 4000$$. - When $F=300$, $$W = 6(300) + 4000 = 1800 + 4000 = 5800$$. 4. **Interpret the range:** The weight $W$ varies from 4000 to 5800 pounds, so the range is $$4000 \leq W \leq 5800$$. 5. **Select the correct answer:** From the given options, the correct set for the range is **the set of all real numbers from 4000 to 5800**. This matches the option: "the set of all real numbers from 4000 to 5800".