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Dynamic Demonstration of Function and Vector Relationships

Dynamic Demonstration of Function and Vector Relationships
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2017-02-15 00:31
VectorFunctionTrigonometryInequalityGeometric Construction
In collections Mapping Diagrams: From AB to C&DE, Resource
This example dynamically demonstrates the relationship between function graphs and vectors, visually showing how changes in the function affect vector direction and magnitude. Core math concepts include functions, vectors, trigonometry, and inequalities. Construction highlights use of GeoGebra commands like Point, Textfield, and Vector to build functions f, vector a, and related points, with sliders for dynamic parameter adjustment. Suitable for high school students learning the integration of functions and vectors, or introductory calculus teaching.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_1
  2. Textfield(f) → inputBox1
  3. Vector(A_1, B_2) → v
  4. Vector(B_2, A_2) → w
  5. Vector(B_2, A_1) → m
  6. Vector(A_2, B_2) → q
  7. Vector(B_2, C) → e
  8. Vector(A_0, A) → h
  9. Vector(A, A_2) → i
  10. Vector(A_0, C) → u
  11. Vector(A_2, C) → z
  12. Vector(A, A_0) → d

AI Drawing Prompt Reference

Create a dynamic illustration showing the relationship between function graphs and vectors, including function plots, vectors, points, and a text field for inputting the function expression. Use sliders to adjust parameters and visually demonstrate how changes in the function affect vector direction and magnitude, incorporating trigonometry and inequalities. Start by plotting points on the coordinate axes, then draw the function graph based on the input expression, create multiple vectors connecting these points, display the function expression in a text field, and finally, use sliders to dynamically adjust parameters to observe the interaction between the function and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.