Answer:

           x    f(x)

         0        0

+2     2      12       +12

+2     4      48       +36

+2     6    108       +60

The function is quadratic. 

The chart displays a rate of change that would indicate such a function. 

Students could recognize the differences between values provided are 12, 36, and 60; the second differences are all 24. 

The fact that the second differences are the same indicates a quadratic function. 

Another strategy would be to look at each of the f(x) values and each are multiples of 3 (3 times 4; 3 times 16; and 3 times 36). 

Note all of the remaining factors (4, 16, and 36) are not only perfect squares, but also perfect squares of the x value. 

This squaring would also indicate a quadratic type of function as well as a possible identity of the function. 

In this problem the function is f(x) = 3x².