The Hyperbola (centered at the origin)
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This example demonstrates the basic hyperbola of the form [math]y = k/x[/math]. Key math concepts include functions, hyperbola, tangent function, limits, quadratic equations, integral calculus, and power functions. Construction highlights the use of GeoGebra commands like If and objects such as a, strA, k, strCoeffSign, strCoeffVal, strMove, text2, text5, e, EquationString, f_1, g_1 for building and adjusting the graph. Suitable for high school and above students to explore the properties and variations of hyperbolas.
GeoGebra Commands & Parameters
If(k < 0, "-", "") → strCoeffSignIf(abs(a) ≟ 1, "", strA) → strCoeffValIf(k ≟ 0, "", If[k > 0, " + " + (abs(k)), " - " + (abs(k))]) → strMove
AI Drawing Prompt Reference
Draw a hyperbola centered at the origin, representing the function y=k/x where k is a constant. Include asymptotes and label key mathematical concepts like functions, hyperbolas, and limits. Allow dynamic adjustment of k to observe changes in the hyperbola. Use text elements to display the function equation and coefficient signs, highlighting the effect of k's sign on the graph.
The prompt above was compiled from the original drawing commands and is for reference only.