INTRODUCTION 

What can the student do with this program?  

  The student can edit and plot three functions: F(x), G(x) and
  H(x) where H(x) is an expression using only F(x) and G(x).  The
  user can also edit and plot parametric equations using a function
  X(x) which determines the position of a point along the X axis. 
  If X(x) = x, then F(x), G(x) and H(x) are plotted as normal
  functions of x.  If X(x) is made to equal something other than x, 
  then the user is operating in a parametric equation mode. 
  Functions can be plotted in rectangular, polar or elliptical
  coordinates.  In rectangular coordinates, the F, G, and H
  function values are plotted as conventional y values.  With polar
  coordinates, the X variable is the same as conventional theta and
  the function values are those of the radius, r.  With elliptical
  coordinates, the X variable is the same as conventional eta and
  the function values are those of xi on a hyperbola.  Edited
  functions and plotting parameters can be saved to a file that is
  created and named by the student.  These exercise files can also
  be saved, loaded, renamed or deleted.  








How does the student select and edit a function?  

  For F(x), G(x) or X(x), the user can select one of five function
  types: polynomial, factored polynomial, trig, exponential or
  logarithmic.  The constants in these expressions can be edited
  over a range of positive and negative values.  By setting some
  constants equal to zero and others equal to one, the functions
  are simplified.  The simplified version of the function is
  written on the screen and updated as the user changes the various
  constants.  The two types called polynomial and factored
  polynomial can be other than true polynomials since they may be
  given negative and fractional exponents.  
 





How does this program help the student to master pre-calculus
mathematics?  

1)  The effects of negative, positive, odd, even and fractional
    exponents are readily observed as well as effects of
    coefficients and additive constants.
2)  Discontinuities of various types are easily illustrated.  
3)  Odd and even symmetry can be demonstrated.  
4)  The powerful effect of using functions of functions can be
    demonstrated to the student in creative and interesting ways.  
5)  Intersections of functions, which are often solutions to
    various types of conditional word problems involving
    simultaneous equations, can be illustrated.  
6)  The concept of a coordinate scale being something other than
    linear is illustrated using elliptical coordinates. 
7)  How a function looks when plotted in rectangular, polar and
    elliptical coordinates are quickly observed and compared.  
8)  A function defined in terms of parametric equations are
    quickly and easily demonstrated.