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Function Continuity Demonstration

Function Continuity Demonstration
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2016-09-08 08:58
FunctionCalculus
In collections BC Calculus Limits & Continuity Limits & Continuity
This example illustrates the definition of continuity of a function f at x=a. By dynamically adjusting the function and point positions, the concept of continuity is intuitively understood. Commands used include Translate, Point, Circle, If, etc. Suitable for high school math education and learning.

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