Visualizing Linearity:
Alternatives to Lines and Planes

Dec. 9, 2013

Martin Flashman
Humboldt State University
Arcata, CA 95521

Descartes  ¤


Example:  Graph and Mapping Diagram

Go to worksheet.

Exploring with a spreadsheet .

 Example: LF.DA.0  with GeoGebra .

For more on linearity [composition and inverses] go to

Example: LF.DFP  with GeoGebra


“Linear” Functions with  two variables
$z=f(x,y) = Ax + By + C$ 

Traditional Approaches to visualizing functions of two variables:

  This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

A 3D Mapping Diagram for a Linear Function of 2 Variables ¤
Example: MFC.0   with GeoGebra

The End


Mapping Diagrams from A(lgebra) B(asics) to C(alculus) and D(ifferential) E(quation)s.
A Reference and Resource Book on Function Visualizations Using Mapping Diagrams