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Continuity Demo: Continuity of Function at a Point

Continuity Demo: Continuity of Function at a Point
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2015-09-14 03:05
FunctionGeometric Construction
In collections Calculus: Limits & Continuity
This example demonstrates the definition of continuity of a function f at x = a using dynamic graphics. Key mathematical concepts include continuity, function graphs, and limits. Construction involves GeoGebra commands like Translate, Point, Circle, and others. Suitable for high school students learning function properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Translate(f, (-3, 0)) → f_1
  2. Translate(g, (3, 0)) → g_1
  3. Point(f_1) → D
  4. Circle((-3, 1), 0.12) → c
  5. Circle((3, 1), 0.12) → d
  6. If(30 ≤ m ≤ 33, Translate[f_1, Vector[((1 / 3 * (m - 30)) * (3, 0))]]) → h
  7. If(30 ≤ m ≤ 33, Translate[c, Vector[((1 / 3 * (m - 30)) * (3, 0))]]) → e
  8. Point(yAxis) → C
  9. Circle(C, 0.12) → k
  10. If(30 ≤ m ≤ 33, Translate[g_1, Vector[((1 / 3 * (m - 30)) * ((-3), 0))]]) → p
  11. If(30 ≤ m ≤ 33, Translate[d, Vector[((1 / 3 * (m - 30)) * ((-3), 0))]]) → q
  12. If(m ≥ 45, Translate[A, Vector[((1 / 8 * (m - 45)) * (0, (-4)))]]) → E

AI Drawing Prompt Reference

Draw a function graph to demonstrate the continuity of a function at x = a. Include two symmetric function images that move left and right, with dots marking key positions. Dynamically show the movement of the function graph and the approach of left and right limits to illustrate the definition of continuity.
The prompt above was compiled from the original drawing commands and is for reference only.