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Explore Graphs of Exponential Functions

Explore Graphs of Exponential Functions
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2019-02-08 04:40
FunctionCalculusDerivativeGraphing
This example demonstrates the dynamic behavior of exponential function graphs as the base changes. Key math concepts include exponential functions, function graph transformations, and derivatives. GeoGebra commands like UnicodeToLetter, Polygon, TableText, LaTeX, Intersect, Sequence, Element, Segment are used, along with objects such as right, left, bottom, top, HowDidIDo, TryAnother, xmark, cmark, etc. It is suitable for high school and above students to understand exponential function properties and graphing techniques.

GeoGebra Commands & Parameters

  1. UnicodeToLetter(10007) → xmark
  2. UnicodeToLetter(10003) → cmark
  3. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  4. TableText({rbDisplay}) → rbLabels
  5. LaTeX(If[a ≟ 1, If[currBaseIndx < 3, (("y=\left(" * Element[rbDisplay, currBaseIndx]) * "\right)^x"), (("y= \vphantom{\dfrac{1}{1}^2}" * Element[rbDisplay, currBaseIndx]) * "^x")], (((("y= \vphantom{\dfrac{1}{1}^2}" * a) * "\left(") * Element[rbDisplay, currBaseIndx]) * "\right)^x")]) → eqnDisp
  6. LaTeX("The graph below depicts a portion of the curve \(y=a\cdot c^x\).\\What do you notice about the \(x\)- and \(y\)-intercepts of the graph?") → MainInstruc
  7. LaTeX("Adjust the values of \(a\) and \(c\) and observe the resulting graph.") → SpecInstruc
  8. Intersect(f, yAxis, (0, 1)) → yIntercept
  9. Sequence((11.5 + i, 4.5), i, 1, 4) → rbPoints
  10. Element(rbPoints, 1) → rb1
  11. Element(rbPoints, 2) → rb2
  12. Element(rbPoints, 3) → rb3
  13. Element(rbPoints, 4) → rb4
  14. Element(rbPoints, currBaseIndx) → currBase
  15. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  16. Segment(legendAnchor, legendAnchor + (1.5, 0)) → legendF