Log translations and dilations：Transformations and Scaling in Geometry
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This example demonstrates how transformations and dilations affect geometric shapes. The key mathematical concepts include geometric transformations, scaling ratios, and shape transformations. Construction involves GeoGebra commands such as vert, hor, base, a, b, text1, text2, text3, f, A, B, C. Suitable for middle or high school mathematics to understand basic concepts of geometric transformations and coordinate geometry.
GeoGebra Commands & Parameters
Numeric vert(1.3)Numeric hor(1.3)Numeric base(2.3)Numeric a(0.0)Numeric b(-1.0)f(x) = b + (vert * log(base, (hor * x) + a))((1 - a) / hor, b + 0)(((-a) + base) / hor, b + vert)(((-a)) / hor + 1 / ((hor * base)), b - vert)
AI Drawing Prompt Reference
Draw a logarithmic function graph defined by vertical and horizontal scaling, a base, and two translation parameters. Set vertical scale to about 1.3, horizontal scale to about 1.3, base to about 2.3, horizontal shift to 0, and vertical shift to -1. Plot the curve, which passes through three key points: the first at the horizontal shift position with y equal to the vertical shift; the second with x determined by the base and horizontal shift, and y equal to vertical shift plus vertical scale; the third with x slightly larger, and y equal to vertical shift minus vertical scale. Include coordinate axes and grid to emphasize the transformation effects.
The prompt above was compiled from the original drawing commands and is for reference only.