Translations of Sinusoidal Functions

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2019-02-21 00:16

Function Trigonometry Graphing

This example demonstrates the translation transformations of sinusoidal function graphs. It covers core math concepts like function graph translation, sinusoidal function properties, and the impact of parameter transformations. The construction uses GeoGebra commands/objects such as UnicodeToLetter, Polygon, LaTeX, Segment, Translate, and objects like HowDidIDo, TryAnother, xmark, cmark, incorrect, correct, isDone, bottomLeft, topLeft, viewbox, showFeedback, h, cos_1, isSinFunc, sin_1, lblCos, lblSin, MainInstruc, lblH, k, lblK, sin_2, cos_2, lblSin_2, lblCos_2, SpecInstruc, legendAnchor1, legendSegment1, legendSegment2. It is suitable for high school mathematics education to understand function graph transformation rules and the meaning of parameters k and h.

GeoGebra Commands & Parameters

UnicodeToLetter(10007) → xmark
UnicodeToLetter(10003) → cmark
Polygon({bottomLeft, (x(bottomLeft), y(topLeft)), topLeft, (x(topLeft), y(bottomLeft))}) → viewbox
LaTeX("f(x)=\cos(x°)") → lblCos
LaTeX("f(x)=\sin(x°)") → lblSin
LaTeX("\text{\textbf{Question: }Given \(g(x)=f(x-h)+k\), how do the characteristics of \(g(x)\) change as \\the values of \(h\) and \(k\) change? Consider amplitude, period, equation of the axis, and range. }") → MainInstruc
LaTeX((("h=" * h) * "^\circ")) → lblH
LaTeX(("k = " * k)) → lblK
LaTeX(("g(x)=" * sin_2)) → lblSin_2
LaTeX(("g(x)=" * cos_2)) → lblCos_2
LaTeX("\text{\textbf{Instructions: }Move the sliders and observe the changes to the graph of \(g(x)\).\\Click `Try Another' to experiment with a different function. ") → SpecInstruc
Segment(legendAnchor1, legendAnchor1 + (90, 0)) → legendSegment1
Translate(legendSegment1, (0, -2)) → legendSegment2