Question

Find a reasonable domain and range for the function. Then graph the function. A car can travel 26 mi for each gallon of gasoline. The function d(x) = 26x represents the distance d(x) in miles, that the car can travel with x gallons of gasonline. The car's fuel tank holds 18 gal.

Choose the correct range below.
O A. 18 <= d(x) <= 468
OB. 0 <= d(x) <= 468
O c. 18 <= d(x) <= 26
OD. 0 <= d(x) <= 18

Answer 1

The correct range for the function is A. 18 <= d(x) <= 468.

To determine the range, we need to consider the possible values for x, which represents the number of gallons of gasoline. Since the car's fuel tank holds 18 gallons, the maximum value for x is 18.

Plugging in the maximum value for x, we get d(18) = 26(18) = 468. This represents the maximum distance the car can travel with a full tank of gasoline.

The minimum value for d(x) occurs when x = 0, which represents the car having no gasoline. In this case, d(0) = 26(0) = 0.

Therefore, the range for the function is 0 <= d(x) <= 468.

To graph the function, we can plot points on a Cartesian coordinate plane. The x-axis represents the number of gallons of gasoline (x) and the y-axis represents the distance in miles (d(x)).

When x = 0, d(x) = 0. This gives us the point (0, 0).

When x = 18, d(x) = 468. This gives us the point (18, 468).

Plotting these points and drawing a line between them, we get the graph of the function.