The dynamic use of technology allows very different ways to visualize graphs and mapping diagrams. The most common ways to do this are through the use of  animations, interactive sliders, and mouse or keyboard controlled movement of objects without sliders. Examples using these tools to give a 21st century approach  to understanding these visualizations will appear throughout this resource  .

Though there are several possible platforms for creating dynamic visualizations, for this introduction to the concepts I will focus mainly on using GeoGebra. Its advantage is that it is open source freeware and  it supports the three main methods for adding dynamic features: animation, sliders, and mouse/keyboard controlled object movement.

Example DTA.0 Animations for Graphs, and Mapping Diagrams

Example DTS.0 : Sliders for Graphs, and Mapping Diagrams

Example DTCOM.0  Controlled Object Movement

See also previous work by Martin Flashman, Yoon Kim, and Ken Yanosko, introducing mapping diagrams with dynamics: Visualizing Functions Pages 2-6
[Add some historical mention of dynagraphs and  uses I've made with Calculus Caculator, WinPlot, and JavaSkechpad.] Other technology resources are listed in the technology reference section.