Question

1. the cost of renting a luxury vehicle, y, for x days can be modeled using a linear function. the rental agency charges a fixed insurance and rental fee of $85, plus an additional $315 per day. the rental agency’s policy requires a minimum of one day of rental but a maximum of eight days of rental. what is the range of the function for this situation?

a. {1, 2, 3, 4, 5, 6, 7, 8}

b. {400, 715, 1030, 1345, 1660, 1975, 2290, 2605}

c. 0 < x ≤ 8

d. 0 < y ≤ 2605

Explanation:

Step1: Define the linear function

The cost function \( y \) for renting a vehicle for \( x \) days is a linear function. The fixed fee is $85 and the daily fee is $315, so the function is \( y = 85 + 315x \).

Step2: Determine the domain of \( x \)

The rental agency requires a minimum of 1 day and a maximum of 8 days, so the domain of \( x \) is \( x \in \{1, 2, 3, 4, 5, 6, 7, 8\} \).

Step3: Calculate \( y \) for each \( x \) in the domain

• For \( x = 1 \): \( y = 85 + 315(1) = 400 \)
• For \( x = 2 \): \( y = 85 + 315(2) = 715 \)
• For \( x = 3 \): \( y = 85 + 315(3) = 1030 \)
• For \( x = 4 \): \( y = 85 + 315(4) = 1345 \)
• For \( x = 5 \): \( y = 85 + 315(5) = 1660 \)
• For \( x = 6 \): \( y = 85 + 315(6) = 1975 \)
• For \( x = 7 \): \( y = 85 + 315(7) = 2290 \)
• For \( x = 8 \): \( y = 85 + 315(8) = 2605 \)

Step4: Determine the range

The range of a function is the set of all possible output values ( \( y \)-values). From the calculations above, the range is the set of these calculated \( y \)-values.

Answer:

B. {400, 715, 1030, 1345, 1660, 1975, 2290, 2605}