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)

PART A

To form the equation to represent total rent, we first need to establish the changing rate and the fixed cost. Changing rate is the fee for every one day the car is rented and fixed cost is the initial cost of the car rental.

To find the changing rate we divide the cost difference between two days by the difference of days

We have 
$180 = 4 days
$ 325 = 9 days

The changing rate is 

The table below shows the working out of the price for each day the car is rented. We work out that day 0 cost $63 which means this is the fixed cost

Hence, the equation of total cost is , where  is the total cost and  is the number of days

PART B:

Using the function notation means we will use  instead of , so the equation is



PART C:

To graph the function, we first need to set the scales on the x-axes and y-axes. 

The scale on x-axes could go up in ones but must start from 0

The scale on y-axes, since it is much bigger values, we can go up in 50

We then plot on the graph for each pair of days and cost. The plots should give us a straight line graph

One example of the graph is shown below

In the first triangle 80+20+p=180 (since sum of all angles of a triangle is 180)so p= 80also in second triangle 55+45+q=180 (since sum of all angles of a triangle is 180)so q=80so we can conclude that p=80 degrees q=80 degrees so p=q=80 degreeshence option b is correct