A car can travel 28 mi for each gallon of gasoline. The function d(x)=28x represents the distance d(x), in miles, that the car can travel with x gallons of gasonline.The car's fuel tank holds 17 gal.
Find a reasonable domain and range for the function. Then graph the function.
Domain: The domain represents the possible values for x, which in this case would be the number of gallons of gasoline. Since the car's fuel tank holds 17 gallons, a reasonable domain would be x ≥ 0 and x ≤ 17.
Range: The range represents the possible values for d(x), which in this case would be the distance the car can travel in miles. Since the car can travel 28 miles for each gallon of gasoline, the range would be the set of all possible distances the car can travel for x gallons of gasoline. A reasonable range would be d(x) ≥ 0.
Graph:
To graph the function, we can plot several points and then connect them with a line. We can choose different values for x, calculate the corresponding d(x), and plot the points.
Let's choose x = 0, 5, 10, 15, and 17.
When x = 0, d(0) = 28(0) = 0. So the first point is (0, 0).
When x = 5, d(5) = 28(5) = 140. So the second point is (5, 140).
When x = 10, d(10) = 28(10) = 280. So the third point is (10, 280).
When x = 15, d(15) = 28(15) = 420. So the fourth point is (15, 420).
When x = 17, d(17) = 28(17) = 476. So the fifth point is (17, 476).
Now, we can plot these points on a graph and connect them with a line.
The graph should show a straight line starting at the origin (0, 0) and passing through the points (5, 140), (10, 280), (15, 420), and (17, 476). The line should continue beyond (17, 476) to represent that the car can continue to travel more than 476 miles, but at this point, the tank is empty.