Final answer:
The function f(g)=3.50g demonstrates that as the number of gallons g increases, the cost f(g) increases, with a domain of 0 ≤ g ≤ 15 and a constant rate of $3.50 per gallon. The maximum cost occurs when the gas tank is full at 15 gallons, totaling $52.50.
Step-by-step explanation:
The gas tank in a car holds 15 gallons and each gallon costs $3.50. The function f(g)=3.50g represents the relationship between the number of gallons of gas purchased, g, and the amount paid for gas, f(g).
A) Complete the statement using <, >, =:
f(5) less than f(6), because as the number of gallons increases, the total cost also increases due to the constant rate of $3.50 per gallon.
B) Find the domain of f(g):
The domain of f(g) is 0 ≤ g ≤ 15, since the gas tank cannot hold more than 15 gallons, and we cannot have a negative quantity of gallons.
C) Find the rate of change of f(g):
The rate of change of f(g) is constant at $3.50 per gallon, as it's a linear function with a slope of 3.50, indicating that the cost increases by $3.50 for each additional gallon.
D) What is f(0)?
f(0) is $0.00, because if no gallons are purchased, no cost is incurred.
E) What is the maximum of f(g)?
The maximum of f(g) is when the tank is full, which is 15 gallons. Thus, the maximum cost is f(15) = 3.50 × 15 = $52.50.