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Interpreting Piecewise Linear Functions 3

Interpreting Piecewise Linear Functions 3
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2020-08-24 16:04
FunctionSequenceCalculusGraphing
① This example demonstrates how to construct and dynamically interpret the graph of a piecewise linear function in GeoGebra, showing the connection of each linear segment and the change of slopes. ② Core mathematical concepts include piecewise functions, linear functions, properties of function graphs, and the idea of upper and lower Riemann sums. ③ Construction highlights: the Sequence command creates a parameter sequence, while the Segment command builds each line segment; key objects are the function graphs g_4, g_2, g_1, g_3, auxiliary points g_{y4}…g_{y1}, parameters t, a, b, c, d, t_1, list2, buttons button1‑button3, and geometric elements road_0, photo_{road}, left_{road}, right_{road}, mid_{road}. ④ Suitable for high‑school mathematics on functions and derivatives, as well as introductory university calculus for visualizing piecewise functions and integral approximations.

GeoGebra Commands & Parameters

  1. Sequence((n, g(n)), n, 0, t_1) → list2
  2. Segment((-1.9, 0), (-1.1, 0)) → road_0
  3. Sequence(i - 0.4 < x < i + 0.4, i, 0, t_1) → photo_{road}
  4. Sequence(x = i - 0.4, i, 0, t_1) → left_{road}
  5. Sequence(x = i + 0.4, i, 0, t_1) → right_{road}
  6. Sequence(x = i, i, 0, t_1) → mid_{road}
  7. Sequence(Translate[car_p, Vector[(0, g(0)), (i - g_y(i), g(i))]], i, 0, t_1) → photo_r
  8. Segment((-1.9, 200), (-1.1, 200)) → road_{200}