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Continuity on a Parabola

Continuity on a Parabola
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2016-12-06 11:42
FunctionCoordinate GeometryCalculus
This example demonstrates continuity on a parabola. It involves the concept of function continuity. Using GeoGebra commands such as f, x0, g, h, etc., the geometric representation of the parabola and its continuity can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. f(x) = 4 - (x - 2)^(2)
  2. Numeric x0(1.6)
  3. x = x0
  4. y = f(x0)
  5. Numeric ep(0.7)
  6. y = f(x0) + ep
  7. y = f(x0) - ep
  8. Numeric delta(0.9)
  9. x = x0 + delta
  10. x = x0 - delta
  11. p(x) = If[x0 - delta ≤ x ≤ x0 + delta, f]