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Rational Inequalities Demo

Rational Inequalities Demo
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2016-08-19 11:38
FunctionCoordinate GeometryInequality
This example demonstrates how to dynamically visualize the solution set and graph behavior of rational inequalities using GeoGebra. It involves core concepts like rational functions, inequality solving, geometric mean, coefficient analysis, polynomial factoring. Key GeoGebra commands and objects used include Textfield, Factor, Simplify, Point, Coefficients, Degree, Sequence, Element, Sort, Length, Polygon, enabling function graphing, factoring, and solution set visualization. Suitable for high school and above mathematics learners to understand the properties and solving methods of rational inequalities.

GeoGebra Commands & Parameters

  1. Textfield(P) → InputBox1
  2. Textfield(Q) → InputBox2
  3. Factor(P) → Pfactor
  4. Factor(Q) → Qfactor
  5. Factor(f) → ffactor
  6. Simplify(P(x) / f(x)) → p
  7. Simplify(Q(x) / f(x)) → q
  8. Textfield(nocommonfactor) → InputBox3
  9. Factor(p) → pfac
  10. Factor(q) → qfac
  11. Point(yAxis) → A
  12. Coefficients(p) → pcoef
  13. Coefficients(q) → qcoef
  14. Degree(p) → pdeg
  15. Degree(q) → qdeg
  16. Textfield(pdegin) → InputBox5
  17. Textfield(qdegin) → InputBox6
  18. Sequence(x = x(Element[list2, i]), i, 1, qdeg) → va
  19. Element(Division[p, q], 1) → quot
  20. Sort(Join[{list1, list2}]) → guidept
  21. Length(guidept) → guideptno
  22. Sort(Join[{guide, guidept}]) → guideptjoin
  23. Sequence(Segment[Element[guideptjoin, i], Element[guideptjoin, i + 1]], i, 1, guideptno + 1) → part
  24. Sequence(Point[Element[part, i]], i, 1, guideptno + 1) → t
  25. Degree(ffactor) → ffactordeg
  26. Sequence(x(Element[Remove[{Root[Q]}, list2], 1]), i, 1, Length[Remove[{Root[Q]}, list2]]) → nondomain
  27. Sequence((x(Element[Remove[{Root[Q]}, list2], i]), g(x(Element[Remove[{Root[Q]}, list2], i]))), i, 1, Length[Remove[{Root[Q]}, list2]]) → holes
  28. Polygon((x(Corner[1]), 0), (x(Corner[2]), 0), Corner[3], Corner[4]) → poly1, f_1, g_1, h_1, i_1
  29. Polygon((x(Corner[1]), 0), (x(Corner[2]), 0), Corner[2], Corner[1]) → poly2, j_1, k_1, l_1, m_1

AI Drawing Prompt Reference

Create a dynamic visualization for rational inequalities, showing input boxes for numerator and denominator, factorization results, and graphs of simplified rational functions. Analyze coefficients and degrees, mark solution sets, represent solution regions with polygons, and handle points where the denominator is zero.
The prompt above was compiled from the original drawing commands and is for reference only.