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Mapping Diagrams - Composite Functions

Mapping Diagrams - Composite Functions
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2017-09-14 23:39
FunctionCoordinate GeometryGraphing
This example demonstrates how mapping diagrams represent the input-output relationships of composite functions. Core math concepts include function mapping, composite functions, and set correspondence. Construction highlights include commands like TableText, Line, Vector, and Sequence from GeoGebra to build dynamic diagrams. Ideal for high school students and teachers to visualize abstract function relationships and composite processes.

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) → InputBox3
  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) → farrows
  28. Zip(Line[ax, ay], ax, arrowxcoords, ay, arrowycoords) → flines
  29. Textfield(g) → InputBox2
  30. Line(OZ, yAxis) → ZaxisLine
  31. Sequence(Text[TableText[{{"\phantom{(}" + (z0 + (n * stepsize)) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(OZ) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] + 7 / unitX, (n * steplength) + y(OZ) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 4 / unitY), true, true], n, ceil((y(Corner[1]) - y(OZ)) / steplength), floor((y(Corner[4]) - y(OZ)) / steplength)) → ZaxisNumbers
  32. Sequence(Segment[(x(OZ), y(OZ) + (n * steplength)), (x(OZ) - 2 / unitX, y(OZ) + (n * steplength))], n, ceil((y(Corner[1]) - y(OZ)) / steplength), floor((y(Corner[4]) - y(OZ)) / steplength)) → ZaxisTicks
  33. Zip(g(f(ax)), ax, arrowxvals) → arrowzvals
  34. Zip((zpos, ((zv - z0) * steplength / stepsize)), zv, arrowzvals) → arrowzcoords
  35. Zip(Vector[ay, az], ay, arrowycoords, az, arrowzcoords) → garrows
  36. Zip(Vector[ax, az], ax, arrowxcoords, az, arrowzcoords) → harrows
  37. Vector((ypos, 0), (zpos, 0)) → v
  38. Zip(Line[ay, az], ay, arrowycoords, az, arrowzcoords) → glines
  39. Zip(Line[ax, az], ax, arrowxcoords, az, arrowzcoords) → hlines

AI Drawing Prompt Reference

Create a mapping diagram for composite functions, including two coordinate systems: one for function f and another for function g. Draw the graph of function f in the input coordinate system and the graph of function g in the output coordinate system. Use arrows to show the mapping relationship between input and output, with arrows pointing from the input coordinate system to the output coordinate system, illustrating the process of composite functions.
The prompt above was compiled from the original drawing commands and is for reference only.