Rational Functions Investigation Tool
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This example demonstrates how to investigate the properties of rational functions using GeoGebra. Key math concepts involved include fractions, rational numbers, incircle or inscribed circle, orthocenter, equations, standard deviation, and piecewise functions. Construction highlights involve using GeoGebra commands/objects like f, g, h, k, a, i, and composite functions fofa, gofa, hofa, kofa. Suitable for high school students and educators to understand the graphs and characteristics of rational functions.
GeoGebra Commands & Parameters
f(x) = (x - 1) / (x^(2) - 1)g(x) = (x^(2) - 1) / (x - 1)h(x) = x / (x^(2) - 1)k(x) = (x^(2) - 1) / xNumeric a(2)x = a(a, f(a))(a, g(a))(a, h(a))(a, k(a))
AI Drawing Prompt Reference
Create a coordinate plane tool for exploring rational functions. Plot four rational function curves: one with a linear numerator and quadratic denominator, one with a quadratic numerator and linear denominator, one with a linear numerator and quadratic denominator, and one with a quadratic numerator and linear denominator. Include a draggable numeric parameter, and draw a vertical dashed line through its value. Mark the corresponding point on each of the four curves at that parameter value, resulting in four distinct points. The graph should dynamically update as the parameter changes, allowing investigation of function behavior.
The prompt above was compiled from the original drawing commands and is for reference only.