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Transformations of Polynomial Functions

Transformations of Polynomial Functions
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2016-10-29 01:30
FunctionTransformation
This example demonstrates the changes in the graph of polynomial functions under various transformations. The key math concepts involved include function transformations, properties of polynomial functions, and the translation and scaling of graphs. The construction utilizes GeoGebra commands and objects such as d, c, a, e, origllabel, translabel, standard, n, transformed, subbed, trans, parent, orig to achieve the transformations and graph plotting. Suitable for high school mathematics education, particularly in teaching and demonstrating function transformations and polynomial functions.

GeoGebra Commands & Parameters

  1. Numeric d(0.0)
  2. Numeric c(0.0)
  3. Numeric a(1.0)
  4. Conic e
  5. Numeric n(2.0)
  6. transformed(x) = (a * (x - d)^(n)) + c
  7. parent(x) = x^(n)

AI Drawing Prompt Reference

Draw a polynomial function and its transformed version through translation and scaling. Start with the basic polynomial function y=x^2, then apply scaling, translation, and vertical translation by adjusting parameters a, d, and c to get the new polynomial function y=a*(x-d)^n+c, and show the original and transformed graphs.
The prompt above was compiled from the original drawing commands and is for reference only.