Dynamic Illustration of Function Input & Output
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This example dynamically illustrates the relationship between function input and output. It visually demonstrates core mathematical concepts such as functions, spheres, centroids, exponents, linear regression, and derivatives. Key GeoGebra commands used include Dilate and Vector to manipulate objects like A, f, g, B, C, a, C', u, B', v, b, c. Suitable for high school and above mathematics education, focusing on function graphs and properties.
GeoGebra Commands & Parameters
Dilate(C, If[0 < a ≤ 1, 1 - a, 0], B) → C'Vector(C, C') → uDilate(B, If[1 < a ≤ 2, 2 - a, 0], A) → B'Vector(B, B') → v
AI Drawing Prompt Reference
Create a dynamic illustration of function input and output. Draw a function curve with two key points representing input and output. Use a slider parameter to move one point along the curve, while the other point moves in the opposite direction based on the same parameter. Show two vectors originating from these points to their new positions, visually demonstrating the mapping relationship and the changes in position and direction.
The prompt above was compiled from the original drawing commands and is for reference only.