Final answer:
To find the interval over which a function f has an average rate of change of zero, more information about the function f and its values at specific points is required.
Step-by-step explanation:
The student is asking about the average rate of change of a function f over a certain interval. The average rate of change is calculated as the change in the function's values (delta y) divided by the change in the interval's values (delta x). When the average rate of change is zero, it means that the function's starting and ending values over the interval are the same, indicating no overall change.
None of the provided information directly gives the intervals for the function f. Therefore, it is necessary to have more information about the function f to determine the interval over which it has an average rate of change of zero.