Answer:
Option C ![f (x) = x^ 2 - 2](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%20x%5E%202%20-%202)
Step-by-step explanation:
Note that the relation describing the set of ordered pairs does not change at a costing rate
![y_2 -y_1 = 7-2 = 5\\\\y_3 -y_2 = 14- 7 = 7\\\\y_4 - y_3 = 23- 14 = 9](https://tex.z-dn.net/?f=y_2%20-y_1%20%3D%207-2%20%3D%205%5C%5C%5C%5Cy_3%20-y_2%20%3D%2014-%207%20%3D%207%5C%5C%5C%5Cy_4%20-%20y_3%20%3D%2023-%2014%20%3D%209)
Therefore the relationship is not linear.
However, the exchange rate
increases by a factor of 2 units when n increases 1 unit. This allows us to conclude that the relationship is quadratic
Note that the following ordered pairs belong to the function
![y = x ^ 2](https://tex.z-dn.net/?f=y%20%3D%20x%20%5E%202)
A = {(2, 4), (3, 9), (4, 16), (5, 25)}
The set of ordered pairs that we have is:
B = {(2, 2), (3, 7), (4, 16), (5, 23)}
Note that there is a similarity between both sets of ordered pairs.
In set B the values of y are always 2 units less than the values in y of the set A.
Then we deduce that since the function that models the set A is
then the function that contains the ordered pairs of the B set is:
![y = x ^ 2 -2](https://tex.z-dn.net/?f=y%20%3D%20x%20%5E%202%20-2)
The correct option is option C) ![f (x) = x^ 2 - 2](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%20x%5E%202%20-%202)