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Solving Equations and Inequalities with Graphing

Solving Equations and Inequalities with Graphing
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2018-07-08 01:26
FunctionInequalityGraphing
This example demonstrates solving equations and inequalities through graphical methods. It covers key concepts such as equations and inequalities, and how to construct these using GeoGebra commands. It includes linear, quadratic, cubic, and radical equations, showcasing various solving techniques. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → lina
  2. Random(-5, 5) → linsol
  3. Intersect(lineq, y = 0) → linint
  4. Random(-5, 5) → quadsol1
  5. Random(-5, 5) → quadsol2
  6. Intersect(quadeq, y = 0) → quadint1, quadint2
  7. Random(-5, 5) → cubsol1
  8. Random(-5, 5) → cubsol2
  9. Random(-5, 5) → cubsol3
  10. Intersect(cubeq, y = 0) → cubint1, cubint2, cubint3
  11. Random(-5, 5) → radsol
  12. Intersect(radeq, y = 0, (-3, 0)) → radint
  13. Random(1, 4) → ineq
  14. Ray(linint, (-10, 0)) → linleft
  15. Ray(linint, (10, 0)) → linright
  16. Intersect(lineq, y = 0) → A
  17. Segment(quadint1, quadint2) → f
  18. If(x(quadint1) < x(quadint2), Ray[quadint1, (-10, 0)], Ray[quadint2, (-10, 0)]) → quadleft
  19. If(x(quadint1) < x(quadint2), Ray[quadint2, (10, 0)], Ray[quadint1, (10, 0)]) → quadright
  20. Intersect(quadeq, y = 0) → B, C
  21. Ray(((-Max[{cubsol1, cubsol2, cubsol3}]), 0), (-10, 0)) → cubleft
  22. Ray(((-Min[{cubsol1, cubsol2, cubsol3}]), 0), (10, 0)) → cubright
  23. If((-cubsol1) < (-cubsol2) < (-cubsol3), Segment[((-cubsol1), 0), ((-cubsol2), 0)], (-cubsol3) < (-cubsol2) < (-cubsol1), Segment[((-cubsol3), 0), ((-cubsol2), 0)], (-cubsol1) < (-cubsol3) < (-cubsol2), Segment[((-cubsol1), 0), ((-cubsol3), 0)], (-cubsol2) < (-cubsol1) < (-cubsol3), Segment[((-cubsol2), 0), ((-cubsol1), 0)], (-cubsol2) < (-cubsol3) < (-cubsol1), Segment[((-cubsol2), 0), ((-cubsol3), 0)], (-cubsol3) < (-cubsol1) < (-cubsol2), Segment[((-cubsol3), 0), ((-cubsol1), 0)]) → h
  24. If((-cubsol1) < (-cubsol2) < (-cubsol3), Segment[((-cubsol2), 0), ((-cubsol3), 0)], (-cubsol3) < (-cubsol2) < (-cubsol1), Segment[((-cubsol2), 0), ((-cubsol1), 0)], (-cubsol1) < (-cubsol3) < (-cubsol2), Segment[((-cubsol3), 0), ((-cubsol2), 0)], (-cubsol2) < (-cubsol1) < (-cubsol3), Segment[((-cubsol1), 0), ((-cubsol3), 0)], (-cubsol2) < (-cubsol3) < (-cubsol1), Segment[((-cubsol3), 0), ((-cubsol1), 0)], (-cubsol3) < (-cubsol1) < (-cubsol2), Segment[((-cubsol1), 0), ((-cubsol2), 0)]) → i
  25. If(cubsol1 ≟ cubsol2 ∧ cubsol1 < cubsol3, Segment[((-cubsol1), 0), ((-cubsol3), 0)], cubsol1 ≟ cubsol3 ∧ cubsol1 < cubsol2, Segment[((-cubsol1), 0), ((-cubsol2), 0)], cubsol2 ≟ cubsol3 ∧ cubsol2 < cubsol1, Segment[((-cubsol2), 0), ((-cubsol1), 0)]) → j
  26. If(cubsol1 ≟ cubsol2 ∧ cubsol1 > cubsol3, Segment[((-cubsol1), 0), ((-cubsol3), 0)], cubsol1 ≟ cubsol3 ∧ cubsol1 > cubsol2, Segment[((-cubsol1), 0), ((-cubsol2), 0)], cubsol2 ≟ cubsol3 ∧ cubsol2 > cubsol1, Segment[((-cubsol2), 0), ((-cubsol1), 0)]) → k
  27. Intersect(cubeq, y = 0) → D, E, F
  28. Segment(((-rada), 0), (radsol, 0)) → l
  29. Ray((radsol, 0), (10, 0)) → m

AI Drawing Prompt Reference

Draw several common types of function graphs including a linear function, a quadratic function, a cubic function, and a radical function, each showing their x-intercepts on the x-axis; use rays and line segments to display the solution intervals for each function on the x-axis, with the linear function having rays extending left and right from its intercept, the quadratic having a segment between its two intercepts and rays extending outward, the cubic having segments between its three intercepts and rays on the outer sides, and the radical function having a segment from its negative root to the solution point with a ray extending to the right.
The prompt above was compiled from the original drawing commands and is for reference only.