Find a reasonable domain and range for the function. Then graph the function.
A car can travel 30 mi for each gallon of gasoline. The function d(x) = 30x represents the distance d(x), in miles, that the car can travel with x gallons of gasonline. The car's fuel tank holds 15 gal.
Domain: The domain of the function is the set of possible values for x, which represents the number of gallons of gasoline. In this case, the car's fuel tank holds 15 gallons, so it would not make sense for x to be a negative number or greater than 15. Therefore, the reasonable domain for this function is the interval [0, 15].
Range: The range of the function is the set of possible values for d(x), which represents the distance traveled in miles. Since each gallon of gasoline allows the car to travel 30 miles, the range would be all the possible distances that are multiples of 30. Therefore, the reasonable range for this function is the set of all non-negative multiples of 30.
Graph: Here is a graph of the function d(x) = 30x over the domain [0, 15].
(Insert graph of a line with x-axis labeled "Gallons of Gasoline (x)" and y-axis labeled "Distance (d)" with the line passing through the points (0, 0) and (15, 450). The line starts at the origin and rises at a constant rate of 30 units on the y-axis for every 1 unit on the x-axis.)
i don't understand
I apologize for any confusion. Here is a simplified explanation:
The domain of the function is the set of possible values for x, which represents the number of gallons of gasoline. In this case, since the car's fuel tank holds 15 gallons, the reasonable values for x would be any number between 0 and 15 (inclusive), because you cannot have a negative number of gallons of gasoline, and it also cannot exceed the tank's capacity.
The range of the function is the set of possible values for d(x), which represents the distance traveled in miles. Since each gallon of gasoline allows the car to travel 30 miles, the distance can be any positive multiple of 30. So the reasonable range for this function is all the possible non-negative multiples of 30.
As for the graph, it would be a straight line starting from the origin (0,0) and rising at a constant rate of 30 units on the y-axis for every 1 unit on the x-axis.