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Interpreting Systems of Piece-wise Linear Functions 3

Interpreting Systems of Piece-wise Linear Functions 3
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2016-07-01 09:18
FunctionTransformationGeometric ConstructionSlider AnimationGraphing
In collections Algebra 1
This GeoGebra example dynamically illustrates a system of piece-wise linear functions and their geometric interpretations, showing how multiple linear segments form rectangles, reflections, and median lines on a plane. The core mathematical concepts include piece-wise linear functions, intersections and region partitioning, linear transformations (rotation and reflection), and geometric objects such as rectangles and conic sections. The construction uses commands like Sequence, Segment, If, and Rotate to generate segmented lines and rotated objects, with interactive buttons (button1, button2, button3) and sliders to toggle visibility, alongside markers and road images for enhanced visualization. It is suitable for high school or early college students learning function graphs, linear programming, and geometric transformations, and serves as an interactive teaching tool for exploring systems of piece-wise linear functions.

GeoGebra Commands & Parameters

  1. Sequence((n, f(n)), n, 0, t_1) → markers_1
  2. Sequence((n, g(n)), n, 0, t_1) → markers_2
  3. Segment((-1.9, 0), (-1.1, 0)) → line_0
  4. Sequence(i - 0.4 < x < i + 0.4, i, 0, t_1) → photo_{road}
  5. Sequence(x = i - 0.4, i, 0, t_1) → left_{road}
  6. Sequence(x = i + 0.4, i, 0, t_1) → right_{road}
  7. Sequence(x = i, i, 0, t_1) → mid_{road}
  8. If(t ≤ 7, 1, -1) → amb_{up}
  9. Segment((-1.9, 200), (-1.1, 200)) → line_{200}
  10. Sequence((n, j(n)), n, 0, t_1) → markers_3
  11. Sequence(Translate[car_p, Vector[(0, j(0)), (i - j_y(i), j(i))]], i, 0, t_1) → photo_c
  12. Sequence(Translate[truck_p, Vector[(0, g(0)), (i - g_y(i), g(i))]], i, 0, t_1) → photo_r
  13. Sequence((i + 0.2, 105), i, 3, t_1) → crashphotos
  14. Rotate(C_1, 180°, C) → G_1
  15. Rotate(C_2, 180°, C) → G_2
  16. Rotate(C_3, 180°, C) → G_3
  17. Sequence(Translate[amb_p, Vector[(0, f(0)), (i, f(i))]], i, 0, Min[t_1, 7]) → photo_a
  18. Sequence(Translate[downamb_p, Vector[(0, f(0)), (i, f(i))]], i, 8, t_1) → photo_d