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Mapping diagrams with adjustable output center

Mapping diagrams with adjustable output center
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2017-08-03 01:10
FunctionGeometric ConstructionGraphing
This example demonstrates how a function can be represented using a mapping diagram instead of a traditional graph, focusing on visualizing function mappings and relationships. It involves core mathematical concepts like function representation, mapping, and geometric intuition. The construction utilizes GeoGebra commands/objects such as TableText, Corner, Distance, Line, Text, panelleft1, Textfield, If, Sequence, Vector, Zip. It is suitable for high school mathematics education to understand different function representations and dynamic changes.

GeoGebra Commands & Parameters

  1. TableText({{"0"}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc") → Xt0
  2. Corner(1) → corner1
  3. Corner(2) → corner2
  4. Corner(3) → corner3
  5. Corner(4) → corner4
  6. Corner(5) → screenDim
  7. Distance(corner1, corner2) → distX
  8. Distance(corner1, corner4) → distY
  9. Line(OY, yAxis) → YaxisLine
  10. Text("(x,y) = (" + (x(A)) + "," + (y(A)) + ") in black coordinate system") → text2
  11. Text("(X,Y) = (" + (x(A) - x(OY)) + "," + (y(A) - y(OY)) + ") in blue coordinate system") → text1
  12. panelleft1(panelsize) → panelquad, panelseg1, panelseg2, panelseg3, panelseg4, panelline
  13. Textfield(f) → InputBox1
  14. Line(OX, yAxis) → XaxisLine
  15. Textfield(x0) → InputBox2
  16. If(minstepfrac > lg(5), 10^(minsteppower + 1), If[minstepfrac > lg(2), (5 * 10^(minsteppower)), If[minstepfrac > 0, (2 * 10^(minsteppower)), 10^(minsteppower)]]) → stepsize
  17. Sequence(Text[TableText[{{"\phantom{(}" + (x0 + (n * stepsize)) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(OX) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] + 7 / unitX, (n * steplength) + y(OX) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 4 / unitY), true, true], n, ceil((y(Corner[1]) - y(OX)) / steplength), floor((y(Corner[4]) - y(OX)) / steplength)) → XaxisNumbers
  18. Sequence(Segment[(x(OX), y(OX) + (n * steplength)), (x(OX) - 2 / unitX, y(OX) + (n * steplength))], n, ceil((y(Corner[1]) - y(OX)) / steplength), floor((y(Corner[4]) - y(OX)) / steplength)) → XaxisTicks
  19. Sequence(Text[TableText[{{"\phantom{(}" + (y0 + (n * stepsize)) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(OY) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] + 7 / unitX, (n * steplength) + y(OY) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 4 / unitY), true, true], n, ceil((y(Corner[1]) - y(OY)) / steplength), floor((y(Corner[4]) - y(OY)) / steplength)) → YaxisNumbers
  20. Sequence(Segment[(x(OY), y(OY) + (n * steplength)), (x(OY) - 2 / unitX, y(OY) + (n * steplength))], n, ceil((y(Corner[1]) - y(OY)) / steplength), floor((y(Corner[4]) - y(OY)) / steplength)) → YaxisTicks
  21. Vector((xpos, 0), (ypos, 0)) → u
  22. Sequence(i / spacing, i, ((-numarrows) * spacing), (numarrows * spacing)) → arrowstarts
  23. Zip(x0 + (as * numminstep), as, arrowstarts) → arrowxvals
  24. Zip(f(ax), ax, arrowxvals) → arrowyvals
  25. Zip((xpos, ((xv - x0) * steplength / stepsize)), xv, arrowxvals) → arrowxcoords
  26. Zip((ypos, ((yv - y0) * steplength / stepsize)), yv, arrowyvals) → arrowycoords
  27. Zip(Vector[ax, ay], ax, arrowxcoords, ay, arrowycoords) → arrows
  28. Zip(Line[ax, ay], ax, arrowxcoords, ay, arrowycoords) → lines
  29. Textfield(y0) → InputBox3
  30. Vector((xpos, 0), (ypos, ((f(x0) - y0) * steplength / stepsize))) → v

AI Drawing Prompt Reference

Create a visual mapping diagram for a function, showing two coordinate systems: a black one and a blue one. Display a point (x,y) in the black system and its corresponding (X,Y) in the blue system. Label the x and y axes with evenly spaced ticks. Use arrows to connect each x-value to its function output y-value, with the tail on the x-axis and head on the y-axis, in different colors for input and output. The diagram should clearly illustrate the function's mapping.
The prompt above was compiled from the original drawing commands and is for reference only.