  Student appreciation of a function is enhanced by understanding the graphical
representation of that function. From the real graph of a polynomial, students
can identify real-valued solutions to polynomial equations that correspond to
the symbolic form. However, the real graph does not show the non-real solutions
to polynomial equations. Instead of enhancing students idea of a function, the
traditional graph implies a clear disconnect from the symbolic form. In order
to fully appreciate the Fundamental Theorem of Algebra, and the non-real
solutions of a polynomial equation, traditional graphs are inadequate. Since
the early 20th century, mathematicians have tried to find a way to augment the
traditional Cartesian graph of a polynomial to show its complex counterpart.
Advancements in computer graphics allow us to easily illustrate a more complete
graph of polynomial functions that is still accessible to students of many
different levels. The authors will demonstrate a method using modern 3D
graphical tools such as GeoGebra to create dynamic visualizations of these more
complete polynomial functions.
