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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!

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Q: What are the steps for finding a function rule if you are given the graph of a function?
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