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Graphing Exponential Functions y = k a^x

Graphing Exponential Functions y = k a^x
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2017-10-03 01:11
FunctionGraphing
This example demonstrates how to graph exponential functions y = k a^x. Key mathematical concepts include the properties and graph characteristics of exponential functions. Using GeoGebra commands such as Simplify and Shuffle, you can dynamically adjust parameters k and a to observe changes in the graph. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Simplify((RandomElement[liste_a]^(x) * Element[liste_k, 1])) → F12
  2. Simplify((RandomElement[liste_a]^(x) * Element[liste_k, 3])) → F11
  3. Simplify((RandomElement[liste_a]^(x) * Element[liste_k, 2])) → F10
  4. Simplify((RandomElement[liste_a]^(x) * Element[liste_k, 1])) → F9
  5. Shuffle({9, 11, 13, 15}) → listshowGf1, {13, 11, 15, 9}
  6. Shuffle({10, 12, 14, 16}) → listshowGf2, {16, 14, 12, 10}
  7. Shuffle({9, 10, 13, 14}) → listshowGf3, {9, 14, 13, 10}
  8. Shuffle({11, 12, 15, 16}) → listshowGf4, {16, 15, 11, 12}
  9. Shuffle({9, 12, 13, 16}) → listshowGf5, {13, 9, 12, 16}
  10. Shuffle({10, 11, 14, 15}) → listshowGf6, {14, 11, 10, 15}
  11. Sequence(If[count < 3, Element[listshowGf0, i], If[count < 5, Element[listshowGf1, i], If[count < 7, Element[listshowGf2, i], If[count < 9, Element[listshowGf3, i], If[count < 11, Element[listshowGf4, i], If[count < 11, Element[listshowGf5, i], Element[listshowGf6, i]]]]]]], i, 1, 4) → listnsG
  12. If(useG, If[count > 2, Random[0, 7], 3], Random[0, 7]) → e'
  13. Random(1, 4) → d
  14. If(count > 2, Random[1, 4], If[count > 1, 3, 1]) → n_g
  15. If(d ≟ e' ∧ (count > 8 ∨ count < 5), 1, e') → e
  16. Random(1, 4) → n_f
  17. Shuffle({1, 2, 3, 4}) → listshowFf1, {4, 1, 3, 2}
  18. Shuffle({1, 4, 5, 8}) → listshowFf2a, {1, 8, 4, 5}
  19. Shuffle({2, 3, 6, 7}) → listshowFf2b, {6, 2, 3, 7}
  20. If(count < 5, Element[listFf, Element[listshowFf1, 3]], If[count < 9, Element[listFf, Element[listshowFf2a, 3]], Element[listFf, Element[listshowFf2b, 3]]]) → f_{3s}
  21. Coefficients(f_{3s}) → listf_{3s}
  22. If(count < 5, Element[listFf, Element[listshowFf1, 4]], If[count < 9, Element[listFf, Element[listshowFf2a, 4]], Element[listFf, Element[listshowFf2b, 4]]]) → f_{4s}
  23. Coefficients(f_{4s}) → listf_{4s}
  24. If(count < 5, Element[listFf, Element[listshowFf1, 1]], If[count < 9, Element[listFf, Element[listshowFf2a, 1]], Element[listFf, Element[listshowFf2b, 1]]]) → f_{1s}
  25. Coefficients(f_{1s}) → listf_{1s}
  26. If(count < 5, Element[listFf, Element[listshowFf1, 2]], If[count < 9, Element[listFf, Element[listshowFf2a, 2]], Element[listFf, Element[listshowFf2b, 2]]]) → f_{2s}
  27. Coefficients(f_{2s}) → listf_{2s}
  28. Element(listCoeffs, n_f, 1) → a_f
  29. Element(listCoeffs, n_f, 2) → b_f
  30. Simplify((-F9(x))) → F13
  31. Simplify((-F10(x))) → F14
  32. Simplify((-F11(x))) → F15
  33. Simplify((-F12(x))) → F16
  34. Sequence(Sequence[(x(A) + (s_p * i), y(A) + (s_p * j)), i, 0, 3], j, 0, 0) → list3CtrofGraphs, {{(5, 0), (13.8, 0), (22.6, 0), (31.400000000000002, 0)}}
  35. Polygon(E, D, F, G) → poly2, e_1, d_1, f_5, g
  36. Polygon(J, K, L, M) → poly4, j, k, l, m
  37. Polygon(J, K, C, B) → poly5, j_1, k_1, c, b_1
  38. Sequence(Sequence[Segment[(x(A) + (s_p * i) - l_x / 2, y(A) + (s_p * j)), (x(A) + (s_p * i) + l_x / 2, y(A) + (s_p * j))], i, 0, 3], j, 0, 0) → list1Xaxes, {{7.6000000000000005, 7.600000000000001, 7.600000000000001, 7.600000000000001}}
  39. Sequence(Sequence[Segment[(x(A) + (s_p * i), y(A) + (s_p * j) - l_y / 2), (x(A) + (s_p * i), y(A) + (s_p * j) + l_y / 2)], i, 0, 3], j, 0, 0) → list2Yaxes, {{10, 10, 10, 10}}
  40. Sequence(Sequence[(x(A) + l_x / 2 + (s_p * i), y(A) + (s_p * j)), i, 0, 3], j, 0, 0) → listXarrow, {{(8.8, 0), (17.6, 0), (26.400000000000002, 0), (35.2, 0)}}
  41. Sequence(Sequence[Text[Element[listChoicestext, i + 1], (x(A) - l_x / 2 + (s_p * (i - 1)), y(A) + l_y / 2)], i, 1, 4], j, 0, 0) → listChoicestextDisplay, {{"(a)", "(b)", "(c)", "(d)"}}
  42. Element(listCoeffs, n_f, 3) → c_f
  43. If(useG, x(Element[listTurningPointsG, Element[listnsG, n_g] - 8]), ((-b_f)) / ((2 * a_f))) → symx2
  44. Defined(root1) → realroots
  45. If(count < 5, Element[listFf, Element[listshowFf1, 4]], If[count < 9, Element[listFf, Element[listshowFf2a, 4]], Element[listFf, Element[listshowFf2b, 4]]]) → f_{tests}
  46. Polygon(B, C, D, E) → poly1, b, c_1, d_2, e_2
  47. If(count < 5, Element[listshowFf1, n_f], If[count < 9, Element[listshowFf2a, n_f], Element[listshowFf2b, n_f]]) → n_s
  48. Sequence(If[count < 5, Element[listshowFf1, i], If[count < 9, Element[listshowFf2a, i], Element[listshowFf2b, i]]], i, 1, 4) → listnsF
  49. Min(d, e) → I1
  50. Min((-d), e) → I2
  51. Min(d, (-e)) → I3
  52. Min((-d), (-e)) → I4
  53. Min(d, e) → I5
  54. Min((-d), e) → I6
  55. Min(d, (-e)) → I7
  56. Min((-d), (-e)) → I8
  57. Max(d, e) → J1
  58. Max((-d), e) → J2
  59. Max((-d), e) → J6
  60. Max(d, (-e)) → J7
  61. Max(d, (-e)) → J3
  62. Max((-d), (-e)) → J4
  63. Max(d, e) → J5
  64. Max((-d), (-e)) → J8
  65. Element(listGf, Element[listnsG, 1] - 8) → g_{1s}
  66. Element(listGf, Element[listnsG, 2] - 8) → g_{2s}
  67. Element(listGf, Element[listnsG, 4] - 8) → g_{4s}
  68. Element(listGf, Element[listnsG, 3] - 8) → g_{3s}
  69. Sequence((0, Cell[7, 8 + i]), i, 1, 8) → listyintercepts
  70. Element(Coefficients[Simplify[Cell[6, Element[listnsG, n_g]]]], 2) → b_g
  71. Element(Coefficients[Simplify[Cell[6, Element[listnsG, n_g]]]], 3) → c_g
  72. Element(Coefficients[Simplify[Cell[6, Element[listnsG, n_g]]]], 1) → a_g
  73. Intersect(f_{1one}, f_{12minusx}) → N

AI Drawing Prompt Reference

Draw the graphs of exponential functions y = k a^x to show how changing parameters k and a affects the graphs. Start by plotting three different exponential function graphs, each with unique k and a values. Then add x and y axes to the coordinate system and label them (a), (b), (c), (d) on the x-axis. Finally, plot the axis of symmetry and vertex of the functions based on their coefficients, and label key points.
The prompt above was compiled from the original drawing commands and is for reference only.