A car rental charge is $100 plus $5.00 per mile traveled. What is the domain and range written as an inequality?

Answer 1

One approach is to sketch a graph, where x is the number of miles driven and y is the total cost.

Your graph will begin where x = zero miles traveled. Note that the question calls for a flat fee of $100, regardless of miles driven, so your graph begins at (0,100). It doesn't make sense to extend the graph into quadrant II, which would indicate negative mileage. The lowest possible value of x, then, is zero. Is there a limit on how many miles you could drive? Well, technically no, though at some point it would certainly be impractical. The problem says nothing about this, so you could show the domain (all possible values of x) as x > 0. x=0 doesn't make sense, since there would be no reason to rent a car and then drive it zero miles.

If the number of miles driven is unlimited, then so is the total cost. As you can see from the graph, y cannot go lower than $100. The range (all possible values of y) begins at $100 and continues infinitely. So your range inequality would be y>100. Here again, y can't reasonable be equal to 100, as this would mean you rented the car but didn't drive it at all, even though this is technically possible.

So, as you can see, there are some practical issues with this problem, as written, but if your teacher disagrees, you now know how to argue the case :)

Best wishes!