Question

The function m(g) provides the number of miles a car can travel on g gallons of gas. The fuel tank holds 14 gallons which allows a maximum ride of 504 miles.

Answer 1

Answer: 0 ≤ g ≤ 14

Explanation:

Answer 2

By Proportionality relationship: A proportionality in which two quantity vary directly to each other.

i,e
`y \propto x`

then; the equation is of the form:
`y =kx` where k is the constant of proportionality.

As per the given statement: The function m(g) provides the number of miles a car can travel on g gallons of gas.

By definition of proportionality, we have;

`m(g) = kg` .....[1] where k is the constant of proportionality.

Also, it is given that the fuel tank holds 14 gallons which allows a maximum ride of 504 miles.

⇒
`g = 14 \text{gallons}` and m(g) = 504 miles

Substitute these in [1] to solve for k;

`504 = 14k`

Divide both sides by 14 we get;

k = 36

Therefore, our equation become:

`m(g) = 36g` where g represents the number of gallons and m(g) represents the distance, in miles

Domain for this equation is; [0,14]

0 represents the empty tank and 14 representing a full tank.

Range: [0, 504]

0 represents the miles traveled on an empty tank and 504 miles represents the distance traveled on a full tank.