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Coordinates, Bar Chart, Dilation, Piecewise Functions, Expected Value Demo

Coordinates, Bar Chart, Dilation, Piecewise Functions, Expected Value Demo
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2017-10-28 06:05
Coordinate GeometryProbability & Statistics
This example demonstrates how to create bar charts using coordinates in GeoGebra, and shows the effect of dilation transformations on piecewise function graphs, while calculating expected values. Core math concepts include coordinate geometry, bar chart creation, dilation transformations, properties of piecewise functions, and expected value computation in probability statistics. Key construction steps involve using commands like Point, Vector, Segment, Line, Derivative, Intersect, Sequence, Zip to build graphics, and sliders for dynamic visualization. Suitable for high school mathematics teaching, focusing on function transformations and statistical calculations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → f_v
  3. Textfield(f) → inputBox1
  4. Vector(x_1, y_1) → v
  5. Segment(f_x, F) → c
  6. Segment(E, F) → d
  7. Segment(A, x_1) → e
  8. Segment(B, y_1) → g
  9. Segment(B, y_1) → h_1
  10. Line(x_1, y_1) → i
  11. Line(A, B) → k
  12. Textfield(f) → inputBox2
  13. Derivative(f) → f'
  14. Vector(B, C) → u
  15. Line(C, D) → b
  16. Intersect(b, k) → Focus
  17. Line(x_1, y_1) → n
  18. Line(A, B) → p
  19. Intersect(n, p) → G
  20. Sequence(n, n, -10, 10) → num
  21. Zip((2, n), n, num) → n_y
  22. Zip((4, n), n, num) → z_h
  23. Vector(A, H) → w
  24. Segment(f_x, E) → m
  25. Point(q) → J
  26. Segment(B, J) → r
  27. Point(B, u) → K
  28. Segment(K, H) → s
  29. Zip((0, y(A) + (h * c)), c, num) → x_h
  30. Zip((2, f(y(A) + (h * c))), c, num) → y_h
  31. Zip(Vector[(0, y(A) + (h * c)), (4, f'(y(A) + (h * c)))], c, num) → df_h
  32. Zip(Vector[(0, y(A) + (h * c)), (2, f(y(A) + (h * c)))], c, num) → f_h
  33. Zip((y(A) + (h * c), f'(y(A) + (h * c))), c, num) → ptdf_h

AI Drawing Prompt Reference

Create a coordinate system with a bar chart and a piecewise function graph, demonstrating the effect of dilation transformations and calculating expected values. Start by drawing the axes and origin, then construct the bar chart based on input function values. Use points, vectors, segments, and lines to build the piecewise function graph, with sliders for dynamic parameter adjustment. Finally, compute and display the expected value, ensuring all elements clearly show the mathematical relationships.
The prompt above was compiled from the original drawing commands and is for reference only.