1 / 36

Functions can not be seen

Functions can not be seen. Rainer Kaenders University of Cologne GeoGebra Conference Linz 2011. Functions can not be seen. … but can be represented GeoGebra can make the identification of functions with their graphs stronger

olin
Télécharger la présentation

Functions can not be seen

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Functionscan not beseen Rainer Kaenders University of Cologne GeoGebra Conference Linz 2011

  2. Functionscan not beseen • … but canberepresented • GeoGebra canmaketheidentificationoffunctionswiththeirgraphsstronger • Many different representations: showthatthereis not therepresentationof a function • Eachrepresentationhas ist ownpossibilitiesandfailures. • GeoGebra ascatalystformathematics!

  3. Functionscan not beseen

  4. Nomograms

  5. Examples Van Dormolen[Dor78], Malle (z.B. in [Mal93], S. 265 oder [Mal00], Spivak ([Spi67], S. 79, www.dynagraph.de Hans-Jürgen Elschenbroich

  6. Examples

  7. Examples

  8. Examples

  9. Examples

  10. Examples

  11. Composition

  12. Composition • IdenticalFunctionhas a naturalappearance • The increase / decreasefrom x to f(x) becomesvisible • Inverse function easy toconstruct • Involutions, f(x) with f  f = id, • Projections, p(x) with p  p = p • CompositionandDecompositionoftwofunctions • Iterationscanbevisualized • General notions on mappingsofsets (injective, surjective, sections, …)

  13. Composition

  14. Linear Functions

  15. Linear Functions

  16. Decomposition

  17. Linear Approximation

  18. A Circle as Derivative Curve

  19. Parabolaas Derivative Curve

  20. Deltoide and

  21. Run alongthe Edge Howtouselevelcurvestorepresentfunctions?

  22. Run alongthe Edge

  23. Toblerone Graph

  24. Outlook

  25. r() = C a

  26. Thankyouforyourattention!

  27. Outline • Functionscan not beseen • Nomogrammes - Composition - Linear Functions - Linear Approximation - Translation of Domain and Value Line - SolvingEquations • Run alongthe Edge - TobleroneDiagram - ProductandSumofFunctions • Outlook - VariousCoordinates

More Related