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Two Graphs for Each Relationship

Two Graphs for Each Relationship
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2020-07-21 22:23
FunctionCoordinate GeometryGraphing
This example demonstrates two graphs for each relationship. Key math concepts include functions and graphing. Commands used include Polygon, PointIn, Ray, Sequence, Text, Segment, etc. Suitable for middle school students to learn how to graph functions.

GeoGebra Commands & Parameters

  1. Polygon((1, 0), (12, 0), (12, 12), (1, 12)) → poly1, f, g, h, i
  2. PointIn(poly1) → A
  3. Ray((0, 0), A) → j
  4. Sequence(Sequence[(i + 0.075, 10.9 - j), j, 1, 10, 1], i, 1, 3, 1) → list3
  5. Sequence(Text[i, (0.25, 10.5 - i)], i, 1, 10, 1) → list1
  6. Sequence((i + 0.35, 10.4), i, 0, 2) → list5
  7. Text(x, Element[list5, 1]) → text0_1
  8. Text(y, Element[list5, 2]) → text0_2
  9. Text(y, Element[list5, 3]) → text0_3
  10. Sequence(Segment[(i, 0), (i, 12)], i, 1, 12, 1) → list6
  11. Sequence(Segment[(0, i), (12, i)], i, 1, 12, 1) → list7
  12. Sequence(Segment[(i, 0), (i, 11)], i, 0, 3.15, 1.05) → list2
  13. Sequence(Segment[(0, i), (3.15, i)], i, 0, 11, 1) → list4
  14. Sequence(Polygon[(1.6, i), (2, i), 4], i, 0.5, 9.5, 1) → list9
  15. Segment((0, 0), (0, y(A))) → k
  16. Segment((0, 0), (x(A), 0)) → l
  17. Polygon((1.85, y(A) / x(A) - 0.5), (2.45, y(A) / x(A) - 0.5), 4) → poly2
  18. Polygon((1.85, y(A) / x(A) - 1.2), (2.45, y(A) / x(A) - 1.2), 4) → poly3
  19. Polygon((x(A) + 0.65, y(A) - 0.55), (x(A) + 1.05, y(A) - 0.55), 4) → poly4
  20. Polygon((x(A) + 0.25, y(A) - 0.55), (x(A) + 0.65, y(A) - 0.55), 4) → poly5
  21. Sequence(Polygon[(1.35, i), (1.7, i), 4], i, 0.05, 9.05, 1) → list10

AI Drawing Prompt Reference

Draw a 12x12 square grid, then randomly select a point A inside the square and draw a ray from the origin to point A. Place 10 equally spaced points on the ray and draw corresponding tick marks on the x-axis and y-axis. Then draw a line segment from the origin to point A, and two slanted lines passing through point A, which intersect the x-axis and y-axis. Finally, draw a series of small rectangles inside the grid, with their vertices intersecting the slanted lines.
The prompt above was compiled from the original drawing commands and is for reference only.