Translate the Square Root Function (IF2-02-CYU4)
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① This interactive example demonstrates the horizontal and vertical translation of the square root function y = √x, where students must plot the transformed function based on given shift amounts. ② Core math concepts include function translation (horizontal shift h and vertical shift k), the graph characteristics of the square root function, and the correspondence between the algebraic expression and its graph. ③ Construction highlights: GeoGebra commands such as If, Polygon, PointIn, Zip, and LaTeX are used to build the interactive interface; objects like startingPoints, usersPoints, and correctPoints track user input and correct answers; gPolyDotted and gPolySolid render dashed/solid polygons for visual checking; feedback, HowDidIDo, and TryAnother provide instant feedback and retry options. ④ Suitable for high school students learning function transformations, and useful for classroom demonstrations or self-paced practice to reinforce intuitive understanding of graph shifts.
GeoGebra Commands & Parameters
If(Random[0, 1] ≟ 0, Random[-6, -1], Random[1, 6]) → kIf(Random[0, 1] ≟ 0, Random[-6, -1], Random[1, 6]) → hPolygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBoxPointIn(viewBox) → BPointIn(viewBox) → APointIn(viewBox) → CZip(A + (h, k), A, startingPoints) → correctPointsLaTeX(UnicodeToLetter[10007]) → xmarkLaTeX(UnicodeToLetter[10003]) → cmarkLaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT