Which of the following is an example of an explicit rule in mathematics?

An explicit rule in mathematics provides a direct way to calculate the output based on the input. In this context, the equation given as y = x + 2 clearly illustrates this concept. It defines a relationship where, for any value of x you substitute into the equation, you can compute the corresponding value of y directly. This straightforward formula allows for immediate evaluation without needing to apply any further operations or transformations.

In contrast, the other choices either do not represent a function that produces an output based purely on an input or do not establish a clear direct relationship. For instance, f(n) = n^2 + 3 also defines a function explicitly, and can calculate outputs directly; however, it is not the choice indicated by the answer provided. The remaining examples involve equations or expressions that do not serve the purpose of an explicit rule as clearly as the chosen equation does.