Black Box Functions
The Antikythera mechanism is an ancient computing device of astonishing complexity and sophistication. Crafted by engineers between 150 and 100 BC, using (what appear to be) Greek theories of astronomy and mathematics, it is the oldest known scientific calculator and has even been called an analog computer. It was recovered in the year 1900 and was found to contain over 30 gears. It was up to scientists, historians, and engineers to reverse engineer the purpose of the device, a feat no doubt comparable to its original construction. 
It is often the case that a device such as the Antikythera cannot be observed directly to figure out how it works. Science is also this way, in that we can observe what happens, but may not know why it happens.
In this exercise, the challenge is to guess the equations for the unknown functions labeled fx, gx, ..., mx by evaluating these functions at various input values and observing the corresponding function values.
To begin, choose a function from the Select a function list. Then evaluate the function at several points by clicking in the plot window. Study the graph as you add points and try to guess the equation for the function. For some of the functions it may be necessary to test many points before the pattern (and hence the equation) becomes clear.
After you have evaluated your function at five or more points, the Check Function button will become available. Before clicking that button, make your guess. Was your guess right? More importantly, was your guess reasonable?
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