Question

A car with 3,000 miles is purchased. The car averages 25 miles per gallon. The linear function m(x) = 25x + 3,000 models the total mileage on the car, m(x), in miles, for a given number of gallons of gas, x. What is the range of the function? [0, ∞) (–∞, ∞) (–∞, 3,000) [3,000, ∞)

Answer 1

The range of the function m(x) = 25x + 3,000, representing the total mileage of the car as a function of gallons of gas used, is the interval [3,000, ∞) since the mileage starts at 3,000 and increases without bound as more gas is used.

Step-by-step explanation:

The range of a function is the set of all possible output values. For the linear function m(x) = 25x + 3,000, which models the total mileage on the car as a function of the number of gallons of gas used, the range would be the set of all possible total mileages that the car can have.

Since the car starts with 3,000 miles, the smallest value that m(x) can have is 3,000. As you add gas and drive, the mileage will increase, so there is no upper limit to the range, given that you can keep adding fuel and driving infinitely. Hence, the range of the function is from 3,000 to infinity, which is represented by the interval [3,000, ∞).