Question

A car rental agency charges a fixed fee plus a daily rate. The function f (x) = 30x + 10 expresses the total cost of renting a car for x days. Suppose the agency doubles the fixed fee and increases the daily rate by $5. Which function represents these changes? A. f(x) = 60 (x + 5) + 10 B.f(x) = 60x + 15 C. f(x) = 30 (x + 5) + 20 D. f (x) = 35x + 20

Answer 1

Writing a function

In the given equation:

f(x) = 30x+ 10, where x is the number of days

We can see that at the beggining, when x = 0, then f (0) = 30 · 0+ 10 = 10

Then, renting a car costs at least $10, so $10 is the fixed fee

Each day that passes $30 is being multiplicated, then it cost $300 per day.

Then, the equation is expressed by

f(x)= daily rate · x + fixed fee

If the agency doubles the fixed fee, it would be that 2 · $10 = $20

If the agency increases the daily rate by $5, in addition, then $30 + $5 = $35 woul be the cost each day.

Then, with these new costs we reaplce our equation

f(x)= daily rate · x + fixed fee

f(x)= 35 · x + 20

Answer: D. f (x) = 35x + 20