Given a set of ordered pairs, it is possible to deduce the formula that describes it, if the function (that describes it) is nonlinear?
For example, if I give you the ordered pairs: $$ (1, 0.0998334166)\\ (3, 0.2955202067)\\ (6, 0.5646424734)\\ $$ Could you tell that $\, sin(.1x)\,$ perfectly describes this list of ordered pairs?
How can I find the equation that describes a list of ordered pairs? (assuming the list of ordered pairs is indeed described by a function, and not just an arbitrary list).
Thanks for your input.
No matter how many points you have, there exists a polynomial that goes through all of them (assuming the $x$ coordinate is unique for each point). The process of finding this polynomial is called polynomial interpolation.
There are other interpolation methods as well, but each of them target some specific output form (such as a sum of sines, piecewise linear functions, etc).
There is no general way of finding a 'simple' function for some definition of simple that fits your points well, such as $\sin(0.1x)$. For each such simple form that you are interested in you can attempt to fit your points to see if it works though.