Presented is a graphical approach to teaching higher degree, rational function, and absolute value inequalities that simplifies the solution of these inequalities and thereby reduces the amount of classroom time that has to be devoted to this topic. Applications are also given for signum functions, maximum-minimum, and points of inflection problems in calculus. The term "wiggle graph" is used to identify the shape of functions produced. Such methods for graphing functions are felt to provide students a way to have a feel for what is going on through seeing how the functions behave. (MP)