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Function Graphing & Ellipse Demo

Function Graphing & Ellipse Demo
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2016-09-06 22:50
VectorFunctionCoordinate GeometryGraphing
This example demonstrates function graphing, ellipse properties, and the geometric relationship between tangents and secants. It involves core math concepts like functions, coordinate geometry, ellipse equations, tangents, secants, and stochastic processes. Constructed using GeoGebra commands like Textfield, Sequence, Vector, Polygon, it's suitable for high school and above mathematics education focusing on function graphs and analytical geometry.

GeoGebra Commands & Parameters

  1. Textfield(xint1') → inputScaleX
  2. Textfield(yint1') → inputScaleY
  3. Textfield(xmin') → inputMinX
  4. Textfield(xmax') → inputMaxX
  5. Textfield(ymin') → inputMinY
  6. Textfield(ymax') → inputMaxY
  7. Textfield(stepX) → InputStepX
  8. Textfield(stepY) → InputStepY
  9. Textfield(labelX) → InputUnitX
  10. Textfield(labelY) → InputUnitY
  11. Textfield(textXa) → InputBox3
  12. Textfield(textYa) → InputBox4
  13. Textfield(textLabel1a) → InputBox1
  14. Textfield(textLabel2a) → InputBox2
  15. Sequence(Sequence[Segment[((xint2 * (j - 1)) + (xint1 * i), ymax), ((xint2 * (j - 1)) + (xint1 * i), ymin)], i, 1, 4], j, 1, ceil(xmax / xint2)) → list5, {{22, 22, 22, 22}, {22, 22, 22, 22}, {22, 22, 22, 22}, {22, 22, 22, 22}, {22, 22, 22, 22}, {22, 22, 22, 22}, {22, 22, 22, 22}, {22, 22, 22, 22}}
  16. Sequence(Sequence[Segment[(((-xint2) * (j - 1)) - (xint1 * i), ymax), (((-xint2) * (j - 1)) - (xint1 * i), ymin)], i, 1, 4], j, 1, ceil(abs(xmin) / xint2)) → list5', {{22, 22, 22, 22}, {22, 22, 22, 22}}
  17. Sequence(Sequence[Segment[(xmin, ((j - 1) * yint2) + (yint1 * i)), (xmax, ((j - 1) * yint2) + (yint1 * i))], i, 1, 4], j, 1, ceil(ymax / yint2)) → list6, {{10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}, {10, 10, 10, 10}}
  18. Sequence(Sequence[Segment[(xmin, ((-(j - 1)) * yint2) - (yint1 * i)), (xmax, ((-(j - 1)) * yint2) - (yint1 * i))], i, 1, 4], j, 1, ceil(abs(ymin) / yint2)) → list6', {{10, 10, 10, 10}}
  19. Sequence(Segment[(0 + (xint2 * i), ymax), (0 + (xint2 * i), ymin)], i, 1, ceil(xmax / xint2)) → list3
  20. Sequence(Segment[(((-xint2) * i), ymax), (0 - (xint2 * i), ymin)], i, 1, ceil(abs(xmin) / xint2)) → list3'
  21. Sequence(Segment[(xmin, (yint2 * i)), (xmax, (yint2 * i))], i, 1, ceil(ymax / yint2)) → list4
  22. Sequence(Segment[(xmin, ((-yint2) * i)), (xmax, ((-yint2) * i))], i, 1, ceil(abs(ymin) / yint2)) → list4'
  23. Vector((x(Export_2), 0), (x(Export_1), 0)) → u
  24. Vector((0, y(Export_2)), (0, y(Export_1))) → v
  25. Polygon(Export_1, (x(Export_1), y(Export_2)), Export_2, (x(Export_2), y(Export_1))) → poly1, export_1, h, export_2, i

AI Drawing Prompt Reference

Draw a function graph and demonstrate the properties of an ellipse along with the geometric relationship between tangents and secants. Start by plotting the coordinate axes with horizontal and vertical grid lines, then sketch the function graph. Next, mark the tangents and secants on the function graph, highlighting their relationship. Finally, use vectors to represent the directions of the tangents and secants, and connect relevant points to form a polygon to emphasize the geometric connection.
The prompt above was compiled from the original drawing commands and is for reference only.