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Function Mapping Diagram

Function Mapping Diagram
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2017-05-09 19:16
FunctionCoordinate GeometryGraphing
This example demonstrates how a function can be represented using a mapping diagram instead of a graph. It involves the concept of functions, particularly how mapping diagrams help understand the input-output relationship. GeoGebra commands used include TableText, Corner, Distance, Line, Text, panelleft1, Textfield, If, Sequence, Vector, Zip, etc. Suitable for high school math education to help students visually understand function properties.

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. Vector((xpos, 0), (ypos, 0)) → v

AI Drawing Prompt Reference

Draw a function mapping diagram to illustrate the input-output relationship of a function. Include two coordinate systems, one black and one blue, labeling the coordinates of points. Mark equal intervals on both axes and connect input and output values with arrows to clearly show the function mapping process.
The prompt above was compiled from the original drawing commands and is for reference only.