A rule is a way of describing a function in words. Conversly, a function is simply a way of describing mathematical rules in numbers and symbols.
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A turtle runs 3 mpm (meters per minute). Write a function rule that shows the total distance the turtle ran for any given amount of time (in minutes, m).
If you know some values, then you at least have a function of some sort, but you don't know what other values might be. To be a useful function you must be aware that a rule exists to calculate its value for any situation, and preferably know what the rule (equation or whatever) is.
A table organizing to imput rule and output of a function
In general, it is impossible. You could try putting together a data set using as many of the points as possible from the graph. Then try various regressions. You may have to perform transformations on the data if the function rule is not straightforward. This could require some very high level statistical techniques. You could be lucky and the graph is a straight line!
Only the function rule. Very complicated patterns may be impossible to discern from a scatter plot or table.