The Freehand Shape Tool lets you either sketch a function, or you can draw a freehand circle, segment or polygon and it will be recognized and converted to an exact shape. If a function f is created, you can compute its value at certain point, place a point on it or perform some transformations. Tangents and derivatives for these functions are not supported.
Notes:
You can use all the curve fitting commands on functions created by this Tool, e.g. FitSin_Command
You can use the Integral command on functions created with this tool e.g. Integral[f, 1, 5] to shade under it and find the area