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Domain and Range Demonstration

Domain and Range Demonstration
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2022-03-20 07:57
FunctionCoordinate GeometryGraphing
This example demonstrates the domain and range of a function. It involves key mathematical concepts such as functions, domain, and range. Using GeoGebra commands like CurveCartesian, Min, Max, etc., the function graph is constructed and its domain and range are observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(r, g(r), r, (-22 * (1 - b)), (22 * (1 - b))) → c
  2. Min(g, -22, -19) → A
  3. Max(g, -15, 0) → B
  4. Segment((0, -10.88), (0, 24.26)) → i
  5. CurveCartesian(q, ((((5 * 0.1) * ((0.2 * q) - 4)) * ((0.2 * q) + 4)) * ((0.2 * q) - 2)), q, -22, 22) → j
  6. CurveCartesian(o, f(o), o, -22, 10) → l
  7. Segment(C, D) → m
  8. CurveCartesian(v, f(v / (1 - b)), v, (-22 * (1 - b)), (10 * (1 - b))) → n
  9. Segment(E, F) → p
  10. Segment((0, -20), (0, 24.65)) → q
  11. Segment((10, -20), (22, 20)) → r
  12. CurveCartesian(w, (((0.5 * ((0.2 * w) - 4)) * ((0.2 * w) + 4)) * ((0.2 * w) - 2)), w, -22, 10) → s
  13. CurveCartesian(z, (((((5 - a) * 0.1) * (((0.2 * z)) / (1 - b) - 4)) * (((0.2 * z)) / (1 - b) + 4)) * (((0.2 * z)) / (1 - b) - 2)), z, -22 + (22 * b), 5 - (5 * b)) → v
  14. Segment(P, O) → f_1
  15. Intersect(f_1, xAxis) → S
  16. Point(yAxis) → T
  17. Segment(S, T) → g_1
  18. CurveCartesian(z, ((((5 * 0.1) * ((0.2 * z) - 4)) * ((0.2 * z) + 4)) * ((0.2 * z) - 2)), z, -22, 5) → w
  19. Segment((10, -15), (22, 2.5)) → h_1

AI Drawing Prompt Reference

Draw a function graph to demonstrate its domain and range. First, plot the function curve, then mark the minimum and maximum values of the domain. Next, draw the boundary lines for the range. Finally, draw the function curves with different parameters to observe their changes within the domain.
The prompt above was compiled from the original drawing commands and is for reference only.