Are the triangles congrouent? if so by what postulate
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Let's analyze the changes made to the parent function one by one:
STEP 1: Horizontal translation.
If we transform
We're performing a change in the form of
This kind of changes result in a horizontal translation, k units to the left if k is positive, k units to the right if k is negative. In this case, k=2, so the original graph is shifted 2 units to the left.
STEP 3: Vertical stretch.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical stretch with scale factor k. If k is negative, the function is also reflected across the x axis. In this case, k=3, so the original graph is stretched vertically, with scale factor 3.
STEP 3: Vertical translation.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical translation, k units down if k is positive, k units up if k is negative. In this case, k= -4, so the graph is shifted 4 units down.
All, in all, the original graph is shifted 2 units to the right, then it's stretched vertically with scale 3, and then it's shifted 4 units down. The order is important!
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
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
PART B:
Using the function notation means we will use
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