For example, if someone draws a circle onto a graph, this will fit an equation of $(x-a)^2+(y-b)^2=r^2$.
However, if someone were to draw another shape, made up of seemingly random points (such as a portrait), would there be an equation that would form the same image if drawn onto a graph?
There are many, many more graphs in the plane than there are formulas we can write down. In fact, since equations must be written in finitely many characters from a finite alphabet, the number of possible equations - or definite descriptions of any kind - we can write is a countable infinity. However, there are uncountably many functions with different graphs on the plane.
Even the most jagged of curves can be given a corresponding Piecewise function,for certain lengths of well known functions . One can also transform known functions to fit the given curve. You could also take some points and try to brute force a function which is true for all the points sampled