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Level Curves

Level Curves
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2018-01-14 20:38
FunctionTrigonometryCoordinate GeometryGraphing
This example demonstrates how to draw and manipulate level curves, showcasing the horizontal cross-sections of a function at different heights; core math concepts include functions, coordinate geometry, trigonometric functions, and geometric transformations; construction highlights involve commands/objects like Line, Point, Midpoint, Mirror, Polygon, Function, Textfield, IntersectPath, ImplicitCurve, Max, Min, Sequence, Derivative; suitable for high school and above students to explore the properties of function graphs and their geometric applications.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → r_1
  2. Line(A, yAxis) → r_2
  3. Point(r_1) → B
  4. Point(r_2) → D
  5. Midpoint(D, B) → M
  6. Mirror(A, M) → C
  7. Polygon(A, B, C, D) → Polígon1, a, b, c, d
  8. Function(f(s, t), s, x(A), x(B), t, y(A), y(D)) → g
  9. Textfield(f) → CampEntradaSortida1
  10. Point(zAxis) → P
  11. IntersectPath(h, f) → i
  12. ImplicitCurve(f(x, y) - f_{(x,y)}) → j
  13. Max(l1) → mx
  14. Min(l1) → mn
  15. Sequence(ImplicitCurve[f(x, y) - s], s, -5, 5, k) → llista1
  16. Point(j) → E
  17. Derivative(f, x) → f_x
  18. Derivative(f, y) → f_y