Question

Write a function to represent the set of ordered pairs.

{(2, 2), (3, 7), (4, 14), (5, 23)}

A) f(x) = x
B) f(x) = 4x - 6
C) f(x) = x 2 - 2
D) f(x) = 2x 2 - 6

Answer 1

Option C
`f (x) = x^ 2 - 2`

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`

Therefore the relationship is not linear.

However, the exchange rate
`y_n- y_(n-1)` 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`

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
`y = x ^ 2` then the function that contains the ordered pairs of the B set is:

`y = x ^ 2 -2`

The correct option is option C)
`f (x) = x^ 2 - 2`