Graphs of f(x), -f(x), and f(-x) for Square Root
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This example demonstrates the graphs of a square root function f(x), its negative -f(x), and its inverse f(-x), highlighting transformations and symmetry. Key math concepts include function graphs, symmetry, and transformations. GeoGebra commands used: f (function), text1, text1_1, text1_2 (text), a, b, c (parameters), g, h (辅助 objects). Suitable for high school mathematics education to understand function transformations and symmetry.
GeoGebra Commands & Parameters
f(x) = sqrt(x)Boolean a(true)Boolean b(false)Boolean c(false)g(x) = (-sqrt(x))h(x) = sqrt((-x))
AI Drawing Prompt Reference
Draw the graph of a square root function, then its negative and its reflection over the y-axis, showing transformations and symmetry, with the original in solid line, the negative and reflected in dashed, and label the expressions and key features.
The prompt above was compiled from the original drawing commands and is for reference only.