Question

Question 3 (Essay Worth 10 points) (03.06 MC) Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325. Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points) Part B: Write the equation obtained in Part A using function notation. (2 points) Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answer 1

First find the slope or rate of change of the cost relative to the number of days.

m=(325-180)/(9-4)

m=145/5

m=29, so far we have:

y=29x+b, using either point we can now solve for b, I'll use (4,180)

180=29(4)+b

180=116+b

64=b so the cost function with respect to days rented is:

y(x)=29x+64

The domain of this function is limited to values greater than or equal to one as renting for zero days, you wouldn't pay the $64 dollar fee and you can't have negative rental days. Furthermore, the range values would be restricted to integer values. And you would have to put some kind of restriction upon how large the values became because you cannot rent a car infinitely...

So the domain would be integer values [0, 30] I just use 30, but you could come to your own conclusion about a logical upper limit to the number of days that the car would be rented. And that would be the domain label to, "days".

The range would also be restricted to integer value starting at 93 and then increasing by multiples of the $29 daily rental fee. Of course this axis is "dollars".