Translation Practice by Glen Reesor

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2015-04-06 11:19

Function Coordinate Geometry

This example demonstrates how to determine the translation parameters h and k given a function and its translated image. Core math concepts include function graph translation, transformation formula g(x)=f(x−h)+k, and analytical geometry. Construction highlights involve Random, If, and Textfield commands, with objects like verticalTranslationProgress, randomFn, k1, h1, etc. Suitable for high school students practicing function transformations and parameter solving.

GeoGebra Commands & Parameters

Random(1, 5) → randomFn
Random(-4, 4) → k1
Random(-4, 4) → h1
If(horizontalStretchProgress < 1, 1 + (horizontalStretchProgress * (abs(bTarget) - 1)), If[horizontalStretchProgress < 1.5, (0.99 * abs(bTarget)), bTarget]) → b
If(verticalStretchProgress < 1, 1 + (verticalStretchProgress * (abs(aTarget) - 1)), If[verticalStretchProgress < 1.5, (0.99 * abs(aTarget)), aTarget]) → a
Textfield(aTarget) → inputBoxa
Textfield(bTarget) → inputBoxb
Textfield(hTarget) → inputBoxh
Textfield(kTarget) → inputBoxk
If(randomFn ≟ 1, (x - h1 - 1)^(2) - 2 + k1, If[randomFn ≟ 2, (1 / 16 * (x - h1)^(3)) - (3 / 4 * (x - h1)) + k1, If[randomFn ≟ 3, (2 * sin(((45 * (x - h1)))°)) + k1, If[randomFn ≟ 4, 2^(x + 1 - h1) - 6 + k1, (((((-1) / 18 * (x + 7 - h1)) * (x + 2 - h1)) * (x - 1 - h1)) * (x - 3 - h1)) + k1]]]) → fnOrig
Random(-7, 7) → h2
Random(-7, 7) → k2