Final answer:
The domain of the function d(x)=32x, which represents the distance in miles that a car can travel using x gallons of gasoline, is 0 ≤ x ≤ 17, as the car's tank holds 17 gallons. The range is 0 ≤ y ≤ 544, as 544 miles is the maximum distance the car can travel on a full tank.
Step-by-step explanation:
The domain of the function d(x)=32x, which represents the distance a car travels on x gallons of gasoline, corresponds to the number of gallons of gasoline that can be put into the car's tank. Since the tank holds 17 gallons, the domain is the set of all real numbers x such that 0 ≤ x ≤ 17, expressed as a compound inequality 0 ≤ x ≤ 17.
As for the range, it corresponds to the distances that the car can travel with 0 to 17 gallons of gasoline. Since the car travels 32 miles per gallon, the maximum distance, when the tank is full (17 gallons), is d(17) = 32 × 17, or 544 miles. Therefore, the range is all real numbers y such that 0 ≤ y ≤ 544, written as the compound inequality 0 ≤ y ≤ 544.