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 domain below.
OA. 0 <= x <= 468 OB. 0 <= x <= 18 OC. 0 <= x <= 26 OD. 18 <= x <= 26
The domain represents the possible values that x can take, which in this case is the amount of gasoline in gallons. Since the car's fuel tank holds 18 gallons, the maximum value that x can be is 18.
Therefore, the correct domain is: 0 ≤ x ≤ 18.
Answer: OB. 0 ≤ x ≤ 18
The correct domain for the function d(x) = 26x, where x represents the number of gallons of gasoline, is 0 <= x <= 18.
Explanation:
Since the car's fuel tank holds 18 gallons, the maximum number of gallons of gasoline that can be used is 18. Therefore, the domain should not exceed this limit. The function d(x) is defined for any number of gallons greater than or equal to 0 and less than or equal to 18. Hence, the correct domain is 0 <= x <= 18.
Note: The range of the function d(x) = 26x is not specified in the question. However, it can be inferred that the range will be all non-negative values as the car can travel a positive distance for any non-negative number of gallons.
To find the domain of the function, we need to consider the possible values that x can take. In this case, x represents the number of gallons of gasoline. Since the car's fuel tank holds 18 gallons, it would not make sense for x to be greater than 18. Therefore, the correct domain for the function would be:
Domain: 0 ≤ x ≤ 18
This means that x can take any value between 0 and 18, inclusive.
Now let's find the range of the function. The range represents the set of possible values for the output or distance traveled (d(x)). In this case, the function d(x) = 26x tells us that the car can travel 26 miles for each gallon of gasoline. Thus, the range would be defined by multiplying the maximum value of x (18) by 26:
Range: 0 ≤ d(x) ≤ (26 * 18) = 0 ≤ d(x) ≤ 468
This means that the distance traveled can take any value between 0 and 468 miles.
Now, let's graph the function. The x-axis will represent the number of gallons of gasoline (x), and the y-axis will represent the distance traveled (d(x)) in miles.
To graph the function, we can plot a few points and then connect them with a straight line. Let's choose some values for x and calculate the corresponding values for d(x):
When x = 0, d(x) = 26 * 0 = 0
When x = 1, d(x) = 26 * 1 = 26
When x = 2, d(x) = 26 * 2 = 52
When x = 18, d(x) = 26 * 18 = 468
Plotting these points on the graph and connecting them gives us a straight line that starts at the origin (0,0) and slopes upward to the right.
So, the correct domain is OA. 0 ≤ x ≤ 468 and the range is 0 ≤ d(x) ≤ 468.