Transformations of Exponential Functions (base change)

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2017-03-10 09:14

This example demonstrates the dynamic transformations of exponential functions under changes in the base, showing effects like translation, scaling, and reflection through parameter adjustments. Key mathematical concepts include exponential functions, function transformations, the impact of base parameters, and geometric transformations. For construction, it utilizes GeoGebra commands such as Root (for finding roots), Extremum (for extrema), Mirror (for reflection), Roots (for multiple roots), and Intersect (for intersections), with objects like base, n, c, b, a as parameter variables to manipulate the function graphs. It is suitable for high school or college-preparatory mathematics courses, ideal for teaching function transformations and parametric plotting.

GeoGebra Commands & Parameters

Root((a * c)) → A
Extremum((a * (x - b)^(2)) + c) → D
Mirror(v, x = 0) → v_1
Mirror(v, y = 0) → v_2
Roots(v, -50, 50) → B,
Intersect(v, x = 0, (0, 1)) → E
Mirror(v, e3) → v_3

AI Drawing Prompt Reference

Draw an exponential function graph showing changes under different bases. Include parameter variables a, c, b, n to adjust the function shape. Key objects are roots, extrema, mirror points, and multiple roots. The construction order is to set parameters, draw the function curve, add symmetry points and roots, then mark extrema.

The prompt above was compiled from the original drawing commands and is for reference only.