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Domain and Range of a Function by Breck Jacobs

Domain and Range of a Function by Breck Jacobs
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2016-03-05 03:45
FunctionCoordinate GeometryGeometric Construction
In collections Chapter 3__Graphing Linear Functions
This example demonstrates how to graphically represent the domain and range of a function using GeoGebra. Key math concepts include functions, domain, range, and geometric constructions. It utilizes commands like If, Min, Max, Intersect, Vector, Defined, Segment, IndexOf, Polygon. Suitable for high school mathematics education or self-study to understand function properties and graphs.

GeoGebra Commands & Parameters

  1. If(a, L, If[b, (1.5, 0), If[c, (1, 0)]]) → L1
  2. If(a, g1, If[b, g2, If[c, g3]]) → f
  3. Min(f, x(L1), rght) → mi11
  4. If(b, (0, 0), If[c, (0.5, 0), If[a, R]]) → R1
  5. Min(f, lft, x(R1)) → mig1
  6. Min(list2) → min_f
  7. Max(f, lft, x(R1)) → mag2
  8. Min(f, x(mag2), x(R1)) → mi_2
  9. Min(y(mi_2), x(mi11)) → MiE
  10. Intersect(f, j, x(mag2), x(mi_2)) → E
  11. Intersect(d, xAxis) → C
  12. Intersect(f, d, (-3, -1.7999999999999998)) → A
  13. Vector(A, B) → u
  14. Defined(A) → e
  15. If(x(L1) ≤ x1, If[x1 < x(R), B, R], L1) → end2
  16. Segment(L1, end2) → h
  17. If(lft ≤ x1, If[x1 < x(R1), B, R1], L) → end1
  18. Segment(L, end1) → g
  19. Intersect(f, j, lft, x(mag2)) → D
  20. Vector((x(L), f(x(L))), L) → v
  21. Vector((x(R), f(x(R))), R) → w
  22. Vector((x(L1), f(x(L1))), L1) → z
  23. Vector((x(R1), f(x(R1))), R1) → l
  24. Max(f, x(L1), rght) → mag22
  25. Max(list1) → max_f
  26. Vector((min_f, f(min_f)), (0, f(min_f))) → r
  27. If(min_f ≤ y1, If[y1 < y(mag2), M, (0, y(mag2))], Y_l) → endv1
  28. Segment(Y_l, endv1) → t
  29. Vector(D, (0, y(D))) → n
  30. IndexOf(max_f, list1) → Ind_ma
  31. IndexOf(min_f, list2) → Ind_mi
  32. Vector(MiPt, (0, y(MiPt))) → v_1
  33. Vector(MaPt, (0, y(MaPt))) → u_1
  34. If(L1 ≠ L, Intersect[f, j, x(L1), rght], Intersect[f, j, x(mi_2), rght]) → F
  35. Vector(E, (0, y(E))) → p
  36. Vector(F, (0, y(F))) → q
  37. If(min_f ≤ y1, If[y1 < y(mag2), (0, y(E)), (0, y(mag2))], (0, MiE)) → endv2
  38. Segment((0, MiE), endv2) → a_1
  39. If(min_f ≤ y1, If[y1 < y(mag22), (0, y(F)), (0, y(mag22))], (0, f(L1))) → endv3
  40. Segment((0, y(L1)), endv3) → b_1
  41. Segment((0, f(L1)), endv3) → c_1
  42. Polygon(Corner[1], (x(Corner[1]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[1])), (x(Corner[4]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[4])), Corner[4]) → poly1, d_1, e_1, f_1, g_1

AI Drawing Prompt Reference

Draw a function graph and indicate its domain and range. First, draw the function graph. Then, use conditional statements to determine the boundary points L1 and R1 for the domain. Find the function values at these boundary points and construct horizontal line segments to represent the range. Finally, use conditional statements and vectors to construct the boundary segments for the domain and range, and the intersection points between them.
The prompt above was compiled from the original drawing commands and is for reference only.