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Parabola, Hyperbola, and Linear Graphs

Parabola, Hyperbola, and Linear Graphs
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2017-05-02 06:36
FunctionCoordinate GeometryGraphing
This example demonstrates the intersection and dynamic behavior of parabolas, hyperbolas, and linear graphs. It involves core math concepts like function graphs, coordinate geometry, linear equations, and properties of quadratic curves. Constructed using GeoGebra commands/objects k, n, f, g, h, p, q, r, m, c, a, b, i, j. Suitable for high school mathematics education to understand function graph intersections and curve properties.

GeoGebra Commands & Parameters

  1. Numeric k(1)
  2. Numeric n(2)
  3. f(x) = (k * x^(n))
  4. g(x) = x^(n) + k
  5. h(x) = (x + k)^(n)
  6. p(x) = k / x
  7. q(x) = 1 / x + k
  8. r(x) = 1 / (x + k)
  9. Numeric m(1.5)
  10. Numeric c(0)
  11. Numeric a(1)
  12. Numeric b(1)
  13. y = (m * x) + c
  14. (a * x) + (b * y) + c = 0

AI Drawing Prompt Reference

Draw the graphs of three power functions: one is the nth power of the x-coordinate multiplied by a constant, another is the nth power of the x-coordinate plus a constant, and the third is the nth power of the x-coordinate plus a constant. Then plot three rational functions: one is a constant divided by the x-coordinate, another is 1 divided by the x-coordinate plus a constant, and the third is 1 divided by the x-coordinate plus a constant. Finally, draw a line with a slope of 1.5 and a line represented by a linear equation to show the intersections and dynamic behavior of these functions with the line.
The prompt above was compiled from the original drawing commands and is for reference only.