One strategy is to pick consecutive inputs, trying to find the pattern to the output. This will help decide if the rule is linear, quadratic, exponential, inverse, or cyclic. Guessing numbers that are in proportion may help as well; if you've tried 10, see what happens with 20.
These algorithms produce the same final result, but may have completely different intermediate steps. One important concern is that the final result is always identical, not just for a few values of the input. Graphically, the functions should be identical, even though they may be created from different steps.