Function Translation Demo
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This example demonstrates the vertical translation of a function f(x) by changing parameter k to generate a new function g(x)=f(x)+k. It involves core mathematical concepts such as function graph translation, quadratic functions, differential calculus (derivative), geometric centroid, and properties of pyramids. The construction uses GeoGebra objects like f (original function), k (translation parameter), g (translated function), h (auxiliary line or point), and a, b (possibly for defining the function or parameter range). Suitable for high school mathematics teaching to understand function transformations and applications of analytical geometry.
GeoGebra Commands & Parameters
f(x) = x^(2)Numeric k(3.4)g(x) = f(x) + kh(x) = (x + k)^(2)Boolean a(false)Boolean b(true)
AI Drawing Prompt Reference
Draw a parabola as the base function and then adjust its vertical position by sliding a parameter to demonstrate function translation. Include auxiliary lines or points and show the images of the original and translated functions to illustrate the core concept of function graph translation in differential geometry.
The prompt above was compiled from the original drawing commands and is for reference only.