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Continuity at a Point

Continuity at a Point
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2019-12-16 20:11
FunctionCalculusLimit
This example demonstrates the continuity of a function at a specific point. Key mathematical concepts include the definition of function continuity. Using GeoGebra commands such as Translate, Point, Circle, etc., the example dynamically shows how the function graph changes around a specific point. Suitable for high school mathematics 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