This task is adapted from "Functions Modeling Change", Connally et al, Wiley 2007. It could also be used as an assessment item. It illustrates examples of functions as well as relationships that are not functions.
This task could be used early on when functions are introduced. The predator-prey example of foxes and rabbits is picked up again in F-IF Foxes and Rabbits 2 and 3 where students are asked to find trigonometric functions to model the two populations as functions of time. Noteworthy is that since the data is a collection of input-output pairs, no verbal description of the function is given, so part of the task is processing what the "rule form" of the proposed functions would look like. This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function, which is violated in the table of values of the two populations. However, this relationship, as shown in the given table of values, cannot possibly be used to present either population as a function of the other. There is a natural (and complicated!) predator-prey relationship between the fox and rabbit populations, since foxes thrive in the presence of rabbits, and rabbits thrive in the absence of foxes.
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