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Create a Linear Function

Create a Linear Function
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2019-05-15 03:21
VectorFunctionCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates how to graph a linear function using GeoGebra, covering core concepts like function graphs, coordinate geometry, and vector operations. Key GeoGebra commands and objects used include Polygon, Segment, If, Sequence, Point, Vector, Join, Element, and AreCollinear. Suitable for high school mathematics instruction to understand the properties and construction of linear functions.

GeoGebra Commands & Parameters

  1. Polygon((1.3, 0), (2.2, 0), 4) → poly2
  2. Polygon((1.3, 1), (2.2, 1), 4) → poly5
  3. Polygon((0, 0), (0.9, 0), 4) → poly1
  4. Polygon((0, 1), (0.9, 1), 4) → poly4
  5. Polygon((1.3, 2), (2.2, 2), 4) → poly8
  6. Polygon((0, 2), (0.9, 2), 4) → poly7
  7. Segment(J, K) → a
  8. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → y1
  9. If(IsInRegion[A, poly7], 1, If[IsInRegion[B, poly7], 2, If[IsInRegion[C, poly7], 3, If[IsInRegion[D, poly7], 4, If[IsInRegion[E, poly7], 5, If[IsInRegion[F, poly7], 6, If[IsInRegion[G, poly7], 7, If[IsInRegion[H, poly7], 8, If[IsInRegion[I, poly7], 9, 0]]]]]]]]) → x1
  10. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → y2
  11. If(IsInRegion[A, poly4], 1, If[IsInRegion[B, poly4], 2, If[IsInRegion[C, poly4], 3, If[IsInRegion[D, poly4], 4, If[IsInRegion[E, poly4], 5, If[IsInRegion[F, poly4], 6, If[IsInRegion[G, poly4], 7, If[IsInRegion[H, poly4], 8, If[IsInRegion[I, poly4], 9, 0]]]]]]]]) → x2
  12. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → y3
  13. If(IsInRegion[A, poly1], 1, If[IsInRegion[B, poly1], 2, If[IsInRegion[C, poly1], 3, If[IsInRegion[D, poly1], 4, If[IsInRegion[E, poly1], 5, If[IsInRegion[F, poly1], 6, If[IsInRegion[G, poly1], 7, If[IsInRegion[H, poly1], 8, If[IsInRegion[I, poly1], 9, 0]]]]]]]]) → x3
  14. Sequence(Point[{i + 0.1, 6}], i, -3, 5) → anchors
  15. Segment((1.1, -0.2), (1.1, 4)) → f
  16. Point({8, -2}) → fakeOrigin
  17. Sequence(Segment[fakeOrigin + ((gridSpacer * i), 0), fakeOrigin + ((gridSpacer * i), (10 * gridSpacer))], i, 1, 10) → verLines
  18. Sequence(Segment[fakeOrigin + (0, (gridSpacer * i)), fakeOrigin + ((gridSpacer * 10), (i * gridSpacer))], i, 1, 10) → horLines
  19. Vector(fakeOrigin, fakeOrigin + ((11 * gridSpacer), 0)) → xaxis
  20. Vector(fakeOrigin, fakeOrigin + (0, (11 * gridSpacer))) → yaxis
  21. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point2anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point2anchor), y(fakeOrigin)) * (1 - i / 300)) + (point2anchor * i / 300), i, 0, 300]}) → path2
  22. Element(path2, timer2) → mover2
  23. AreCollinear(point1anchor, point2anchor, point3anchor) → line
  24. Polygon((-0.3, -0.3), (2.5, -0.3), (2.5, 3.2), (-0.3, 3.2)) → region, h, i, j, k
  25. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point3anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point3anchor), y(fakeOrigin)) * (1 - i / 300)) + (point3anchor * i / 300), i, 0, 300]}) → path3
  26. Element(path3, timer3) → mover3
  27. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point1anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point1anchor), y(fakeOrigin)) * (1 - i / 300)) + (point1anchor * i / 300), i, 0, 300]}) → path1
  28. Element(path1, timer1) → mover1
  29. If(¬firstCheck, Line[mover1, mover2], Line[newMover1, newMover2]) → g
  30. Point({x(fakeOrigin) - gridSpacer, g(x(fakeOrigin) - gridSpacer)}) → leftBound
  31. Point({x(fakeOrigin) + (11 * gridSpacer), g(x(fakeOrigin) + (11 * gridSpacer))}) → rightBound
  32. If(¬firstCheck, Vector[mover1, leftBound], Vector[newMover1, leftBound]) → u
  33. If(¬firstCheck, Vector[mover1, rightBound], Vector[newMover1, rightBound]) → v
  34. If(¬firstCheck, timer3 ≟ Length[path3], checkedTimer ≟ 1) → ready

AI Drawing Prompt Reference

Draw a graph of a linear function with multiple square grids. Connect points based on their positions within specific regions to form line segments, showcasing the function's graph. Start by creating horizontal and vertical square grids. Then, determine and connect points to form the function's graph. Finally, add coordinate axes and boundary points to complete the illustration.
The prompt above was compiled from the original drawing commands and is for reference only.