Find a reasonable domain and range for the function. Then graph the function. A car can travel 29 mi for each gallon of gasoline. The function d(x) = 29x represents the distance d(x) in miles, that the car can travel with x gallons of gasonline. The car's fuel tank holds 10 gal. Choose the correct domain below. A. 0 <= x <= 290 B. 0 <= x <= 29 OC. 10 <= x <= 29 OD. 0 <= x <= 10
The car's fuel tank holds 10 gallons, so the maximum number of gallons the car can have is 10. Therefore, the correct domain is: D. 0 <= x <= 10.
To find the range, we can plug in different values for x into the function d(x) = 29x.
When x = 0, the car has no gasoline and can't travel any distance (0 miles).
When x = 10, the car has a full tank of gasoline and can travel 29 miles for each of the 10 gallons, so it can travel a total of 290 miles.
Therefore, the range is: 0 <= d(x) <= 290.
Graphing the function will show a line with a slope of 29 passing through the point (0,0). The x-axis will represent the number of gallons of gasoline (x) and the y-axis will represent the distance traveled (d(x)). As x increases from 0 to 10, the distance traveled (d(x)) will increase from 0 to 290.
Here is a graph of the function:
*[illustration graph]
To find the reasonable domain for the function, we need to consider the practical restrictions on the number of gallons of gasoline. The question states that the car's fuel tank holds 10 gallons of gasoline. Therefore, the number of gallons of gasoline (x) should be within the range of 0 to 10, since you cannot use negative gallons or more than the tank's capacity.
So, the correct domain for this function is OD.
As for the range, we can use the given function d(x) = 29x to determine how far the car can travel for different values of x.
Substituting x = 10 (the maximum number of gallons the tank can hold), we find the maximum distance the car can travel: d(10) = 29 * 10 = 290 miles.
Therefore, the reasonable range for this function is 0 to 290 miles.
Now, let's graph this function.
To graph the function, we need to plot points on a coordinate plane, where the x-axis represents the number of gallons of gasoline (x) and the y-axis represents the distance traveled (d(x)).
We already know that for each gallon of gasoline, the car can travel 29 miles. So, we can plot the following points:
(x, d(x)) = (0, 0), (1, 29), (2, 58), (3, 87), (4, 116), (5, 145), (6, 174), (7, 203), (8, 232), (9, 261), (10, 290)
The graph will be a straight line passing through these points.
I apologize, as a text-based AI, I'm unable to provide a visual graph. However, you can plot the points on a graph paper or using an online graphing tool to visualize the function.
The correct domain for the function is option D: 0 <= x <= 10.
This is because the car's fuel tank can hold up to 10 gallons of gasoline, so the number of gallons of gasoline used cannot exceed 10. Therefore, the domain of the function should be limited to 0 gallons (no gasoline) up to 10 gallons (full fuel tank).
Now let's find the range for the function:
The function d(x) = 29x represents the distance d(x) in miles traveled with x gallons of gasoline.
Since the car can travel 29 miles for each gallon of gasoline, the range of the function will be dependent on the number of gallons used. As the car can hold up to 10 gallons of gasoline, the maximum distance it can travel is 29 * 10 = 290 miles.
Therefore, the range for the function is 0 <= d(x) <= 290.
To graph the function, plot the points that represent different values of x and d(x). Start from the origin (0, 0), then plot the point (10, 290) as the maximum distance the car can travel with a full fuel tank. Finally, draw a line connecting these two points, which will represent the function d(x) = 29x on the graph.
The graph should start at the point (0, 0) on the x-y coordinate system and form a straight line that passes through the point (10, 290).