Explore Function Translations
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This example demonstrates function translations, involving key mathematical concepts such as functions and translation. By adjusting parameters a, h, and k, observe the translation effects on the function graph. The construction summary mentions objects including function f and its translated functions f1, f2, and f3. Suitable for high school math education or student self-study on function transformations.
GeoGebra Commands & Parameters
f(x) = xNumeric a(1)f_{1}(x) = (a * f(x))Numeric h(1)f_{2}(x) = f(x - h)Numeric k(1)f_{3}(x) = f(x) + k
AI Drawing Prompt Reference
Draw a graph showing function translations. Start with a straight line through the origin as the base function. Then add three transformed versions: one stretched vertically by a scale factor, one shifted horizontally by a distance, and one shifted vertically by a distance. Display all four curves together, using distinct colors or line styles, with adjustable parameter sliders nearby to observe the translation effects.
The prompt above was compiled from the original drawing commands and is for reference only.