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Find a and b for Function Continuity

Find a and b for Function Continuity
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2015-08-16 06:10
FunctionSlider Animation
This example demonstrates a function with two unknowns. By adjusting sliders to choose the correct values of the two unknowns, the function becomes continuous at a specified point. Key mathematical concepts include function continuity. The construction uses objects such as a, b, f1, f2, f3, and f.

GeoGebra Commands & Parameters

  1. Numeric a(3.1)
  2. f1(x) = -2
  3. Numeric b(-3.9)
  4. f2(x) = (a * x) + b
  5. f3(x) = 2
  6. f(x) = If[x ≤ -1, f1, If[-1 < x < 3, f2, f3]]

AI Drawing Prompt Reference

Draw a piecewise function where for x ≤ -1, the function value is -2; for -1 < x < 3, the function value is ax+b, with a set to 3.1 and b set to -3.9; and for x ≥ 3, the function value is 2. Adjust a and b to make the function continuous at x = -1.
The prompt above was compiled from the original drawing commands and is for reference only.