Download the following Mathematica notebook ( .nb) files:

Orbit.nb - computes the orbit of the the given point under the given function.
Doubling.nb - formula and graph of the doubling function.
Convergence.nb - computes the orbit of the the given point under the given function until it gets close to a given fixed point or a 2-cycle. Returns the orbit and number of iterates.
NumSolutions.nb - use it to graph and solve equations numerically if you don't have a graphing calculator.
Orbit_diagram.nb - computes the asymptotic orbit of the the given point under the function with given parameter value c and plots it on cx-plane.
Full_orbit_diagram.nb - sketches the complete orbit diagram; you select the initial point and the size of the plot.