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Sign Diagram Demo

Sign Diagram Demo
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2011-09-25 21:05
FunctionCalculusInequality
This example demonstrates how to use a sign diagram to analyze the positivity and negativity of functions across different intervals. It involves core math concepts like inequalities, subtraction, power functions, squares, and real numbers. Constructed using GeoGebra commands such as Intersect, Segment, and If, it is suitable for high school mathematics teaching to help students understand function properties and inequality solving methods.

GeoGebra Commands & Parameters

  1. Intersect(g, y = 0) → A
  2. Segment(A, C) → p
  3. Intersect(f_2, y = 0) → B
  4. Segment(B, D) → q
  5. If(f_2(x) < 0, fneg) → q_1
  6. If(f_2(x) > 0, fpos) → r
  7. If(seco(x) < 0, gneg) → s
  8. If(seco(x) > 0, gpos) → t
  9. If(f_2(x) * seco(x) < 0, ftimesgneg) → f_1
  10. If(f_2(x) * seco(x) > 0, ftimesgpos) → g_1
  11. Intersect(seco, y = 0) → E_1
  12. Segment(E_1, F) → j
  13. If(f_2(x) * h_1(x) / seco(x) < 0, treneg) → r_1
  14. If(f_2(x) * h_1(x) / seco(x) > 0, trepos) → s_1
  15. If(h_1(x) < 0, hneg) → t_1
  16. If(h_1(x) > 0, hpos) → g_2
  17. Intersect(h_1, y = 0) → E
  18. Segment(E, G) → e