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Rational Function Curve Sketching

Rational Function Curve Sketching
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2016-07-13 16:39
FunctionCalculusGeometric Construction
Demonstrates the construction of a rational function curve by showing and hiding different elements. This example covers the concept of rational functions and the properties of asymptotes. GeoGebra commands such as objects f, Asymptote1, Asymptote2 are used in the construction. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. f(x) = (((x + 1) * (x - 2))) / (((x - 3) * (x + 2)))
  2. Asymptote1(x) = If[-2.2 ≤ x ≤ -1.8, f]
  3. Asymptote2(x) = If[2.8 ≤ x ≤ 3.2, f]
  4. Small(x) = If[-100 ≤ x ≤ -8, f]
  5. Large(x) = If[8 ≤ x ≤ 100, f]
  6. (0, 1 / 3)
  7. (-1, 0)
  8. (2, 0)
  9. y = 1
  10. x = -2
  11. x = 3
  12. Middle(x) = If[-2 ≤ x ≤ 3, f]
  13. Left(x) = If[-20 ≤ x ≤ -2, f]
  14. Right(x) = If[3 ≤ x ≤ 20, f]

AI Drawing Prompt Reference

Sketch a rational function curve with asymptotes. First, draw the function f(x) = (x + 1)(x - 2) / (x - 3)(x + 2). Then, draw the vertical asymptotes at x = -2 and x = 3, and the horizontal asymptote at y = 1. Next, draw the local image of the function near the x-axis, and the magnified images on both sides of the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.