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Describing Transformations of Radical Functions

Describing Transformations of Radical Functions 1.3 - Solution

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A graph is horizontally stretched or shrunk when you multiply the xx value of the function by a factor a.a. Additionally, a vertical translation happens when a constant is added to the function. Vertical translation:f(x)+kHorizontal stretch/shrink:f(ax)\begin{aligned} \textbf{Vertical translation:}& \quad f(x)+k \\ \textbf{Horizontal stretch/shrink:}& \quad f(ax) \\ \end{aligned} Regarding the vertical translation, if the constant is positive, the graph shifts upwards. Therefore, it's true that g(x)g(x) is a translation 33 units up of the parent square root function. However, when a<1a<1 in f(ax),f(ax), we have a horizontal stretch (away from the xx-axis) and not a shrink.