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+4000 gives Was 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: ▼ ? 00 Oweight of airplane (in pounds) Oamount of fuel in airplane's tank (in gallons) (Choose one) Range: ▼ X 5 Oweight of airplane (in pounds) (Choose one) Oamount of fuel in airplane's tank (in gallons)

Answer 1

In the function \( W = 5F + 4000 \), where \( W \) is the total weight of the airplane in pounds and \( F \) is the total amount of fuel in its tank in gallons, we can analyze the relationships between weight and fuel.

Domain

The domain of the function refers to the allowed values for \( F \). Since the fuel tank can hold up to 200 gallons, \( F \) can take on any value from 0 to 200 gallons. Thus, the correct description for the values in the domain is:

• Amount of fuel in airplane's tank (in gallons)

Range

The range of the function refers to the possible values for \( W \) which is determined by the equation \( W = 5F + 4000 \).

1. When \( F = 0 \): \[ W = 5(0) + 4000 = 4000 \text{ pounds} \]

2. When \( F = 200 \): \[ W = 5(200) + 4000 = 1000 + 4000 = 5000 \text{ pounds} \]

The weight \( W \) will vary from 4000 pounds to 5000 pounds as \( F \) varies from 0 to 200 gallons. Therefore, the range consists of weights between 4000 and 5000 pounds. Thus, the correct description for the values in the range is:

• Weight of airplane (in pounds)

Summary

• Domain: Amount of fuel in airplane's tank (in gallons)
• Range: Weight of airplane (in pounds)

Answer 2

what is the set of values

Answer 3

Based on the analysis of the function \( W = 5F + 4000 \), we can define the sets of values for both the domain and the range as follows:

Domain

The domain \( F \) (the total amount of fuel in the tank) is limited as follows:

• Minimum value: \( 0 \) gallons (empty tank)
• Maximum value: \( 200 \) gallons (full tank)

Set of Values for the Domain: \[ F \in [0, 200] \quad \text{(in gallons)} \]

Range

The range \( W \) (the total weight of the airplane) changes based on the values of \( F \):

• When \( F = 0 \): \( W = 4000 \) pounds
• When \( F = 200 \): \( W = 5000 \) pounds

The weight will thus vary between 4000 pounds to 5000 pounds.

Set of Values for the Range: \[ W \in [4000, 5000] \quad \text{(in pounds)} \]

Summary:

• Domain: \( [0, 200] \) gallons (amount of fuel)
• Range: \( [4000, 5000] \) pounds (weight of airplane)