Question

the fuel tank of a certain airplane can hold up to 300 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 (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)|the set of all real numbers from 4000 to 5500
the set of all real numbers from 0 to 300
the set of all real numbers from 5 to 4000
{0, 1, 2, 3,ldots,4000}
{300, 301, 302, 303,ldots}
{300, 301, 302, 303,ldots,5500}|

Explanation:

Step1: Identify the domain

The domain of a function is the set of all possible input - values. Here, the input variable is $F$ which represents the amount of fuel in the airplane's tank. Since the fuel tank can hold up to 300 gallons of fuel and the amount of fuel cannot be negative, the domain is the amount of fuel in the airplane's tank (in gallons) and the set of values is the set of all real numbers from 0 to 300.

Step2: Identify the range

The range of a function is the set of all possible output - values. The function is $W = 5F+4000$. When $F = 0$, $W=5\times0 + 4000=4000$. When $F = 300$, $W=5\times300+4000=1500 + 4000=5500$. So the range is the weight of the airplane (in pounds) and the set of values is the set of all real numbers from 4000 to 5500.

Answer:

Domain:
Description of Values: amount of fuel in airplane's tank (in gallons)
Set of Values: the set of all real numbers from 0 to 300
Range:
Description of Values: weight of airplane (in pounds)
Set of Values: the set of all real numbers from 4000 to 5500