Answer:
Option C [tex]f (x) = x^ 2 - 2[/tex]
Step-by-step explanation:
Note that the relation describing the set of ordered pairs does not change at a costing rate
[tex]y_2 -y_1 = 7-2 = 5\\\\y_3 -y_2 = 14- 7 = 7\\\\y_4 - y_3 = 23- 14 = 9[/tex]
Therefore the relationship is not linear.
However, the exchange rate [tex]y_n- y_{n-1}[/tex] 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
[tex]y = x ^ 2[/tex]
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 [tex]y = x ^ 2[/tex] then the function that contains the ordered pairs of the B set is:
[tex]y = x ^ 2 -2[/tex]
The correct option is option C) [tex]f (x) = x^ 2 - 2[/tex]
