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Let $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x+4}-2$.

Which of the following transformations have been applied to $f(x)$ in order to obtain $g(x)$? Select ALL that apply.

Shifted up $2$ units

Shifted down $2$ units

Shifted right $4$ units

Shifted left $4$ units

Horizontally stretched by a factor of $4$

Horizontally compressed by a factor of $4$