Reflection of y=e^x
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TRANSFORMATION OF FUNCTIONS
This example demonstrates the geometric relationship between the function y=e^x and its reflected image. Core math concepts include function graphs, reflection transformations, and properties of exponential functions. Construction highlights the use of GeoGebra objects: a (point), f (function), g (reflected function), h (auxiliary line or point), text1 (text label), text3 (text label). Suitable for high school students learning and understanding function transformations, especially the symmetry of exponential functions.
GeoGebra Commands & Parameters
Numeric a(1.0)f(x) = ℯ^((a * x))g(x) = log((a * x))y = (a * x)
AI Drawing Prompt Reference
Draw the graph of the function y=e^x, then draw its reflected image y=log(ax) with a set to 1. Start by creating point a, then draw the function f(x)=e^(a*x), followed by the function g(x)=log(a*x). Finally, add an auxiliary line or point h to illustrate the reflection relationship.
The prompt above was compiled from the original drawing commands and is for reference only.