Find a reasonable domain and range for the function. Then graph the function. A car can travel 31 mi for each gallon of gasoline. The function d(x) = 31x represents the distance d(x) in miles, that the car can travel with x gallons of gasonline. The car's fuel tank holds 12 gal. Choose the correct domain below. OA. 0 <= x <= 372 OB. 12 <= x <= 31 OC. 0 <= x <= 12 OD. 0 <= x <= 31
The correct domain for the function is 0 <= x <= 12
Explanation:
The domain of a function represents the set of all possible input values (x-values) for the function. In this case, the function represents the distance the car can travel with x gallons of gasoline. The car's fuel tank holds 12 gallons, so the maximum number of gallons of gasoline that can be input into the function is 12. Therefore, the domain of the function is 0 <= x <= 12.
The range of the function represents the set of all possible output values (y-values) for the function. In this case, the function d(x) = 31x represents the distance in miles that the car can travel. The car can travel 31 miles for each gallon of gasoline, so the range of the function is 0 <= d(x) <= 31 * 12.
To graph the function, you can plot the points (x, d(x)) with x-values between 0 and 12 and calculate the corresponding d(x) values using the function.
The correct domain for this function is OC: 0 <= x <= 12.
Explanation: Since the car's fuel tank holds 12 gallons, the maximum number of gallons of gasoline the car can have is 12. Therefore, the domain of the function should not exceed this maximum value.
Additionally, the domain cannot be negative or go beyond what is physically possible, so the domain must start at 0. Hence, the reasonable domain for this function is from 0 to 12 gallons: 0 <= x <= 12.
To find the reasonable domain, we need to consider the restrictions on the variable "x" in the given context. In this case, "x" represents the number of gallons of gasoline.
According to the information given, the car's fuel tank can hold a maximum of 12 gallons. Therefore, the number of gallons of gasoline, represented by "x," cannot exceed 12 gallons. In other words, "x" must be less than or equal to 12.
So, the correct domain for the function is 0 <= x <= 12 (option OC).
Now, let's find the reasonable range, which represents the possible values the output (distance traveled) can take.
The function d(x) = 31x tells us that for each gallon of gasoline, the car can travel 31 miles. Since the function is a linear equation, the range is the set of all possible distances the car can travel.
In this case, the car can travel a minimum of 0 miles (if there is no gasoline in the tank, x = 0) and a maximum of 31 * 12 = 372 miles (if the tank is full, x = 12). Therefore, the reasonable range for this function is 0 <= d(x) <= 372.
Finally, let's graph the function. Plot the values of x and d(x) on a coordinate plane, where x is the horizontal axis and d(x) is the vertical axis.
You will have points (0, 0) and (12, 372) representing the minimum and maximum values. Then, draw a straight line between these two points to represent the relationship between distance and gallons of gasoline.
The graph will start at (0, 0) and rise by a slope of 31, indicating that for each gallon of gasoline, the car can travel 31 miles.
Therefore, the correct domain is 0 <= x <= 12 (option OC), and the reasonable range for this function is 0 <= d(x) <= 372.