Gallery for Families of Functions

The following is a gallery of demos for illustrating selected families of 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 'bulk' 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, 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. 

Polynomials, Power Functions, & Rational Functions

Constant functions, y = c
GSP
  Vary c: Gif Animation     Mov Animation
Linear functions,
y = mx + b
GSP

Vary m: Gif Animation     Mov Animation

Vary b: Gif Animation      Mov Animation

Absolute value functions,
y = a |x - b| + c
GSP
Vary a: Gif Animation      Mov Animation

Vary b: Gif Animation      Mov Animation

Vary c: Gif Animation      Mov Animation

Greatest integer functions,
y = a [bx - c]
GSP
Vary a: Gif Animation      Mov Animation

Vary b: Gif Animation      Mov Animation

Vary c: Gif Animation      Mov Animation

Quadratic function
y = ax2 + bx + c
GSP

Vary a: Gif Animation      Mov Animation

Vary b: Gif Animation      Mov Animation

Vary c: Gif Animation      Mov Animation

Quadratic function
y = a(x - h)2 + k
GSP

Vary a: Gif Animation      Mov Animation

Vary h: Gif Animation      Mov Animation

Vary k: Gif Animation      Mov Animation

Cubic function
y = ax3+bx2+cx+d
GSP

Vary a: Gif Animation      Mov Animation

Vary b: Gif Animation      Mov Animation

Vary c: Gif Animation      Mov Animation

Vary d: Gif Animation      Mov Animation

Square Root

GSP

Vary a: Gif Animation     Mov Animation

Vary b: Gif Animation     Mov Animation

Vary c: Gif Animation      Mov Animation

Cube Root

GSP

Vary a: Gif Animation     Mov Animation

Vary b: Gif Animation     Mov Animation

Vary c: Gif Animation      Mov Animation

Power function

GSP
Vary b: Gif Animation     Mov Animation

Reciprocal function

GSP

 

Vary a: Gif Animation     Mov Animation

Vary b: Gif Animation     Mov Animation

 

Reciprocal of x2 function

GSP
Vary a: Gif Animation     Mov Animation

Vary b: Gif Animation     Mov Animation

 

Reciprocal of x3 function

GSP

Vary a: Gif Animation     Mov Animation

Vary b: Gif Animation     Mov Animation