Chapter 4 - An Introduction to Functions - 4-5 Writing a Function Rule - Practice and Problem-Solving Exercises - Page 266: 30

The function rule for this relation is r(d)=$\frac{1}{2}$$d^{2}$.

The function is non linear, so the power on d is 2 as when d=4, $d^{2}$=$4^{2}$=16. Half of 16 is 8 and plus one is 9. Thus when d=4, r=9. The function was derived this way as you had to square the value of d, then half it and then add one.