Question

Find a reasonable domain and range for the function. Then graph the function:

A car can travel 31 miles for each gallon of gasoline. The function d(x) = 31x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. The car's fuel tank holds 18 gallons.
a) Domain: x ≥ 0, Range: d ≥ 0
b) Domain: x ≤ 0, Range: d ≤ 0
c) Domain: x ≤ 18, Range: d ≤ 558
d) Domain: x ≥ 18, Range: d ≥ 558

Answer 1

The reasonable domain and range for the function d(x) = 31x, with a car's fuel tank capacity of 18 gallons, are Domain: 0 ≤ x ≤ 18 and Range: 0 ≤ d(x) ≤ 558. The graph is a straight line from (0, 0) to (18, 558).

Step-by-step explanation:

We are given a function d(x) = 31x where d(x) represents the distance in miles that the car can travel using x gallons of gasoline. Since a car's fuel tank can hold 18 gallons, the domain is the set of all possible gallons of gasoline that can be put in the tank, so the domain should be 0 ≤ x ≤ 18. The range is the set of all possible distances the car can travel with up to 18 gallons, which corresponds to the distance the car travels with a full tank, so the range should be 0 ≤ d(x) ≤ 558 (since 31 miles/gallon * 18 gallons = 558 miles).

To graph the function, you would plot a straight line from (0, 0) to (18, 558), showing that as you increase the number of gallons (x-axis), the distance (y-axis) increases linearly. The line would end at the point (18, 558) reflecting the maximum capacity of the fuel tank and the maximum distance possible with a full tank.

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