Polar vs Rectangular Functions

Slide the point, A, along the rectangular graph, and observe the corresponding polar motion. You can change the function f(x) by entering f(x)= and your new function. Be careful about the range of f, since many functions will go off the image....
Notice what happens to r, as f(x) goes from positive to negative, and observe how "loops" are made.

Dave Matthews, April 9. 2007, Created with GeoGebra