A.4.A.10.27TN

Answer to Problem 27:  

 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.