Sarah is renting a car for her weekend trip to the mountains. The total cost of the rental, f(x), in relation to the number of miles driven, x, is illustrated in the graph due today.

To provide an appropriate response to your question, I would need to have the graph mentioned. Since you've described the graph as "due today," but haven't included it here for reference, I am unable to directly interpret or analyze the specific cost function f(x) in relation to the number of miles, x, for Sarah's car rental. If you can provide the graph or at least a description of the graph, I'd be happy to help you understand how the total cost of the rental changes with the number of miles driven.

Extra: The cost of renting a car is often related to both a base fee and a variable fee based on usage. Commonly, car rental companies charge a certain amount per day for the rental of the car (the base fee) and then an additional fee for each mile driven over a given limit (variable fee).

Let's explain the basic concept with a hypothetical example. Assume there is a car rental company that has the following fee structure: - A flat fee of $50 for the weekend rental. - An additional $0.25 per mile after the first 100 miles are driven.

A function representing this cost structure could look something like this:

f(x) = $50 + $0.25(x - 100) for x > 100

If Sarah drove 150 miles, the total cost would be calculated as: f(150) = $50 + $0.25(150 - 100) = $50 + $0.25(50) = $50 + $12.50 = $62.50

Now, in a graph of such a function, the line would start at $50 (the base fee) and stay flat until 100 miles have passed. After 100 miles, the line would slope upwards at a rate of $0.25 per mile, which represents the additional cost per mile driven.

Understanding these principles would help a student determine the cost based on the mileage should they have access to the specifics of the given graph.