Question

the fuel tank of a certain airplane can hold up to 200 gallons of fuel. let w be the total weight of the airplane (in pounds). let f be the total amount of fuel in its tank (in gallons). suppose that w = 5f + 3000 gives w as a function of f. identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.

description of values

set of values

| domain: | weight of airplane (in pounds)
amount of fuel in airplanes tank (in gallons) | select |
| range: | weight of airplane (in pounds)
amount of fuel in airplanes tank (in gallons) | select |

Explanation:

Step1: Determine Domain Description

The function is \( W = 5F + 3000 \), where \( W \) depends on \( F \). The domain is the input variable, which is \( F \) (amount of fuel in gallons). So Domain description: amount of fuel in airplane’s tank (in gallons).

Step2: Determine Domain Set of Values

The fuel tank can hold up to 200 gallons, and \( F \) can't be negative. So domain set: \( 0 \leq F \leq 200 \) (or values from 0 to 200 gallons, inclusive).

Step3: Determine Range Description

The range is the output variable, which is \( W \) (weight of airplane in pounds). So Range description: weight of airplane (in pounds).

Step4: Determine Range Set of Values

Substitute \( F = 0 \): \( W = 5(0) + 3000 = 3000 \). Substitute \( F = 200 \): \( W = 5(200) + 3000 = 1000 + 3000 = 4000 \). So range set: \( 3000 \leq W \leq 4000 \) (or values from 3000 to 4000 pounds, inclusive).

Answer:

• Domain Description: amount of fuel in airplane’s tank (in gallons)
• Domain Set of Values: \( 0 \leq F \leq 200 \) (or equivalent set like \(\{F | 0 \leq F \leq 200, F \text{ is a real number}\}\))
• Range Description: weight of airplane (in pounds)
• Range Set of Values: \( 3000 \leq W \leq 4000 \) (or equivalent set like \(\{W | 3000 \leq W \leq 4000, W \text{ is a real number}\}\))

(For the table selection:

• Domain: select "amount of fuel in airplane’s tank (in gallons)" and set of values \( 0 \leq F \leq 200 \) (or the option with 0 to 200 gallons)
• Range: select "weight of airplane (in pounds)" and set of values \( 3000 \leq W \leq 4000 \) (or the option with 3000 to 4000 pounds))