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Transformations of Exponential Functions by cemccourseware

Transformations of Exponential Functions by cemccourseware
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2019-03-20 00:32
FunctionCalculus
This example demonstrates the transformations of exponential function graphs, including translations, stretches, and reflections. It covers core math concepts like exponential function properties, function transformations, and coordinate systems. Constructed using GeoGebra commands such as If, Shuffle, Element, LaTeX, UnicodeToLetter, Textfield, with objects like ansB, k, h, wholeList, aWhole, etc. Suitable for high school mathematics education to understand transformation rules of exponential functions.

GeoGebra Commands & Parameters

  1. If(Random[1, 2] ≟ 1, Random[-7, -1], Random[1, 7]) → k
  2. If(Random[1, 2] ≟ 1, Random[-7, -1], Random[1, 7]) → h
  3. Shuffle(1…4) → wholeList
  4. Element(wholeList, 1) → aWhole
  5. If(Random[1, 2] ≟ 1, aWhole, 1 / aWhole) → aWholeFrac
  6. If(Random[1, 2] ≟ 1, (aWholeFrac * (-1)), aWholeFrac) → a
  7. Element(wholeList, 2) → bWhole
  8. If(Random[1, 2] ≟ 1, bWhole, 1 / bWhole) → bWholeFrac
  9. If(Random[1, 2] ≟ 1, (bWholeFrac * (-1)), bWholeFrac) → b
  10. If(b ≟ -1, "-", If[b ≟ 1, "", NumToImproperFrac[b]]) → txtB
  11. LaTeX(((((txtB * "\left(x") * If[c ≟ 0, "", If[(b * h) < 0, "-", "+"]]) * NumToImproperFrac[abs(h)]) * "\right)")) → txtInnerFactored
  12. UnicodeToLetter(10007) → xmark
  13. UnicodeToLetter(10003) → cmark
  14. Textfield(textA) → ansAbox
  15. Textfield(textH) → ansHbox
  16. Textfield(textK) → ansKbox
  17. LaTeX("\text{Vertical \hspace{140} by a factor of}") → verStretchCompress2
  18. LaTeX("\text{Reflection in the \(x\)-axis}") → reflectX
  19. LaTeX("\text{Translation \hspace{80} by \hspace{50} unit(s)}") → horTranslate2
  20. LaTeX("\text{Translation \hspace{80} by \hspace{50} unit(s)}") → verTranslate2
  21. LaTeX("\text{Vertical translation}") → verTranslate1
  22. LaTeX("\text{Vertical stretch or compression}") → verStretchCompress1
  23. LaTeX("\text{Horizontal translation}") → horTranslate1
  24. Textfield(textB) → ansBbox
  25. LaTeX("\text{Reflection in the \(y\)-axis") → reflectY
  26. Shuffle({2, 3, 4, 5, 1 / 2, 1 / 3, 1 / 4, 1 / 5}) → possibleBaseValues
  27. Element(possibleBaseValues, 1) → base
  28. LaTeX((("\text{\textbf{Question: }Identify the transformations.\\\textbf{Instructions: }Select and describe all of the transformations that are applied to \(f(x)=(" * FractionText[base]) * ")^x\)\\to obtain the function shown below.}")) → TEXT
  29. LaTeX((((txtB * "x") * If[h ≟ 0, "", If[(b * h) > 0, "-", "+"]]) * NumToImproperFrac[abs((b * h))])) → txtInnerExpanded

AI Drawing Prompt Reference

Draw a graph demonstrating transformations of exponential functions, including translations, stretches, and reflections. Randomly generate a vertical stretch factor and a horizontal translation, then plot the base exponential function and its transformed versions. Label key transformation parameters like the vertical stretch factor and horizontal translation distance, with text annotations explaining each type of transformation. Start with the base function, then sequentially show the effects of translation, stretch, and reflection, finally labeling each parameter and type of transformation.
The prompt above was compiled from the original drawing commands and is for reference only.