Polynomial & Rational Function Gallery

The following is a gallery of demos for illustrating selected families of polynomials and rational functions. These animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions for functions. Two file formats, gif and mov are available.

  1. The gif animations should run on most systems and the file sizes are relatively small. 

  2. The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.) 

  3. The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.

  4. We use abbreviations, GSP for Geometer's Sketch Pad 4 and EX for Excel spread sheet, VB for visual basic, and J for java to indicate the software used to generate the frames of the animation. If alternate corresponding software is also available there will be more than one abbreviation in that category. The VB software routines can be executed and the others can be downloaded.

Polynomials, Power Functions, & Rational Functions

Constant functions, y = c
GSP
also EX and VB files
  Vary c: Gif Animation 
            Mov Animation
Click to execute the VB file  
Linear functions,
y = mx + b
GSP
also EX and VB files

Vary m: Gif Animation  
             Mov Animation

Vary b: Gif Animation  
            Mov Animation

Click to execute the VB file  
Absolute value functions,
y = a |x - b| + c
GSP
also EX, VB, and J files
Vary a: Gif Animation 
            Mov Animation

Vary b: Gif Animation 
            Mov Animation

Vary c: Gif Animation  
            Mov Animation

Click to execute the VB file Click to execute the java applet
Greatest integer functions,
(or step functions)
y = a [bx - c]
GSP
also an EX file
Vary a: Gif Animation  
            Mov Animation

Vary b: Gif Animation  
            Mov Animation

Vary c: Gif Animation 
            Mov Animation

   
Quadratic functions,
(or parabolas)
y = ax2 + bx + c
GSP
also EX, VB, and J files

Vary a: Gif Animation  
           Mov Animation

Vary b: Gif Animation  
           Mov Animation

Vary c: Gif Animation  
           Mov Animation

Click to execute the VB file Click to execute the java applet
Quadratic functions,
(or parabolas)
y = a(x - h)2 + k
GSP
also EX, VB, and J files

Vary a: Gif Animation  
           Mov Animation

Vary h: Gif Animation   
            Mov Animation

Vary k: Gif Animation   
            Mov Animation

Click to execute the VB file Click to execute the java applet
Cubic function
y = ax3+bx2+cx+d
GSP
also EX, VB, and J files

Vary a: Gif Animation 
            Mov Animation

Vary b: Gif Animation 
            Mov Animation

Vary c: Gif Animation   
            Mov Animation

Vary d: Gif Animation 
            Mov Animation

Click to execute the VB file Click to execute the java applet
Square Root

GSP
also an EX and a J file

Vary a: Gif Animation
            Mov Animation

Vary b: Gif Animation 
            Mov Animation

Vary c: Gif Animation  
            Mov Animation

  Click to execute the java applet
Cube Root

GSP
also an EX file

Vary a: Gif Animation  
            Mov Animation

Vary b: Gif Animation 
            Mov Animation

Vary c: Gif Animation   
            Mov Animation

   
Power function

GSP
also a J file
Vary b: Gif Animation 
            Mov Animation
  Click to execute the java applet

Reciprocal function

GSP
also an EX file

 

Vary a: Gif Animation
            Mov Animation

Vary b: Gif Animation 
            Mov Animation

   
Reciprocal of x2 function

GSP
also an EX file
Vary a: Gif Animation 
            Mov Animation

Vary b: Gif Animation 
            Mov Animation

   
Reciprocal of x3 function

GSP
also an EX file

Vary a: Gif Animation 
            Mov Animation

Vary b: Gif Animation  
            Mov Animation

   

Zipped downloads ==>

Download (all) Animation files (large file)

Download (12) Geometer's Sketchpad files

Download (12) Excel files

Download (6) Java applets

 

Other Selected Resources:

Credits: 

 

8/10/03DRH          Last updated  2/11/2005

As of 8/28/03