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
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.
To find a reasonable domain and range for the function, let's analyze the given information:
We are given that the car can travel 26 miles for each gallon of gasoline. This means that for each gallon of gasoline, the car can go a distance of 26 miles.
The function d(x) = 26x represents the distance d(x) in miles that the car can travel with x gallons of gasoline.
Next, we are told that the car's fuel tank holds 18 gallons.
From this information, we can determine the domain and range of the function:
Domain: The domain represents the possible values for x, which in this case is the number of gallons of gasoline. Since the car's fuel tank holds 18 gallons, the reasonable domain for this function would be x = 0 to x = 18.
Range: The range represents the possible values for d(x), which is the distance the car can travel. Since each gallon of gasoline allows the car to travel 26 miles, and the car's fuel tank holds a maximum of 18 gallons, the reasonable range for this function would be d(x) = 0 to d(x) = 26 * 18 = 468.
Based on the explanation above, the correct range for this function is:
OB. 0 <= d(x) <= 468
To graph the function, you would use a Cartesian coordinate system with gallons of gasoline (x) as the independent variable on the x-axis and the distance traveled (d(x)) as the dependent variable on the y-axis. The graph would be a straight line with a positive slope, starting from the origin (0,0) and extending to the point (18, 468).
The correct range for the function d(x) = 26x, where x is the number of gallons of gasoline, is:
A. 18 <= d(x) <= 468
To find the domain and range of the function, we need to consider the limitations of the car's fuel tank. The car's fuel tank can hold a maximum of 18 gallons of gasoline, so the domain for the function would be 0 <= x <= 18.
To find the range, we can substitute the limits of the domain into the function:
d(0) = 26(0) = 0
d(18) = 26(18) = 468
Therefore, the reasonable range for the function is 0 <= d(x) <= 468.
Now let's graph the function. Plot points for different values of x and d(x) on a coordinate plane:
(0, 0), (1, 26), (2, 52), (3, 78), (4, 104), (5, 130), (6, 156), (7, 182), (8, 208), (9, 234), (10, 260), (11, 286), (12, 312), (13, 338), (14, 364), (15, 390), (16, 416), (17, 442), (18, 468)
Connect these points with a straight line, and you will have the graph of the function d(x) = 26x.