Does this table represent a function? why or why not?

By definition we have to:

 A mathematical function is a relationship that is established between two sets, through which each element of the first set is assigned a single element of the second set or none.
 The initial set or starting set is also called the domain; the final set or set of arrival, meanwhile, can be called codomain.

 For this case, the table represents a function and the function is linear because the rate of change (slope) is constant and equal to 200.

 
 option D

(6^2)^4

(12^3)^2

(36^2)^2

(3^2)^7

(9^3)^2