Question

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

Answer 1

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]