Graphs and Mapping Diagrams

Martin Flashman

Visualizing Functions with Mapping Diagrams and Graphs. Functions defined on R and RP1=S1, the circle.


  • 1. Graph of a function RP1 -> RP1
  • 2. 3 Dimensional Mapping Diagram for z= f(x,y)
  • 3. Mapping Diagram of Function : RP1 to RP1
  • 4. 3D Mapping Diagram for linear z=f(x,y) with focus point
  • 5. Graph w/ Mapping diagram: Estimating The Derivative
  • 6. Mapping Diagrams (Real) Visualize Solving a Quadratic Equation
  • 7. Mapping Diagrams To Visualize Solving a Linear Equation
  • 8. Mapping Diagrams To Visualize Solving a Linear Equation
  • 9. (a,b) is an open interval
  • 10. Mapping Diagram, Spreadsheet, Graph, Realign, Focus
  • 11. Visualizing Numeric Transformations

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Graph of a function RP1 -> RP1

The graph of a function is the set of ordered pairs of elements of RP^1. We consider RP^1 to be S^1, the circle, so the graph is a subset of S^1 x S^1 : the torus.
– Martin Flashman

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