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A graph is horizontally stretched or shrunk when you multiply the $x$ value of the function by a factor $a.$ Additionally, a vertical translation happens when a constant is added to the function. \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 $g(x)$ is a translation $3$ units up of the parent square root function. However, when $a<1$ in $f(ax),$ we have a horizontal stretch (away from the $x$-axis) and not a shrink.