# Car rental cost function graph

An economy car rented in Florida from Enterprise on a weekly basis costs $185$ per week. Extra days cost $37$ per day until the day rate exceeds the weekly rate, in which case the weekly rate applies. Also any part of a day used counts as a full day. Find the cost C of renting an economy car as a function of the number x of days used, where $7 \le x \le 14$. Graph this function.

From what I understand I made the following piecewise function.

$$f(x) = \begin{cases} 185 & x=7\\[2ex] 185+(x-7)(37) & 7<x<14\\[2ex] 370 & x=14 \end{cases}$$

What would the graph be for this ?

• Are you sure you got the function right? How much would it cost to rent the car 13 days? – David Sep 20 '15 at 23:32
• @David I edited the function. I'm guessing it is right now ? – RufioLJ Sep 21 '15 at 0:08

The current version of the function is not right. As @David implied, you do not correctly handle the fact that anything between $11$ and $14$ days will be billed the same as $2$ weeks, due to the "until the day rate exceeds the weekly rate" clause. You also do not handle $x$ being a non-integer: it should be rounded up.
$$f(n)=\begin{cases} 185+37(\lceil x\rceil-7), & 7\le x\le 11 \\[2 ex] 370, & 11<x\le 14 \end{cases}$$
where $\lceil x\rceil$ is the ceiling function, rounding up to the smallest integer greater than or equal to $x$.
The ceiling function means that each small section of the graph, of width $1$, will be a horizontal line. The second case means that the last part of the graph is a horizontal line between $x=11$ exclusive to $x=14$ inclusive. The first case means that the segments will be like a staircase, with the left-hand endpoints on the line $y=185+37x$. Here is a graph.