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Combination of Function Graph Transformations: Stretch and Translation

Combination of Function Graph Transformations: Stretch and Translation
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2019-11-27 04:54
FunctionTransformationGraphing
This example demonstrates the combined effect of stretching and translating function graphs. Key mathematical concepts include function graph transformations, stretching, and translation. Using GeoGebra commands such as Min, If, and SurdText, the transformation process is dynamically illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Min(f, -12, 12) → A
  2. Min(p, -12, 12) → B
  3. If(h < 0, "+", "-") → text17
  4. SurdText(h / q) → text18
  5. Expand(f_1) → g_1

AI Drawing Prompt Reference

Draw the graph of the function f(x) = sin(x) and apply transformations of stretching and translation. First, stretch f(x) by a factor of h/q along the y-axis, then translate it by |h| units along the x-axis. Next, plot the transformed function g(x) = sin(x * h / q) + h. Finally, dynamically show how changes in h and q affect the graph.
The prompt above was compiled from the original drawing commands and is for reference only.