Question

Sabrina is planning a trip abroad. The cost of the flight is 350, and she will spend up to 5 nights at a hotel at the same nightly rate of75. The function f(x) = 75x + 350 represents the relationship between the total cost of the trip based on x, the number of nights in a hotel. What is the range of the function for this situation?

Answer 1

The range of the function f(x) = 75x + 350 representing the total cost of Sabrina's trip abroad, given she stays between 0 and 5 nights in a hotel, is from $350 to $725.

Step-by-step explanation:

The student's question asks about the range of the function f(x) = 75x + 350, where x represents the number of nights Sabrina spends in a hotel for a trip she is planning abroad, and f(x) represents the total cost of the trip. Since the hotel cost per night is $75 and the flight is $350, and she will stay for up to 5 nights, we can find the range of total costs by plugging in the values of x from 0 to 5 in the function. For 0 nights, the cost would be f(0) = 75(0) + 350 = $350 (just the flight). For 1 night, the cost would be f(1) = 75(1) + 350 = $425, and we can continue calculating up to 5 nights. For 5 nights, f(5) = 75(5) + 350 = $725. Therefore, the range of f(x) for Sabrina's trip abroad, given that she stays between 0 and 5 nights, is [$350, $725].