Write an equation for the function whose graph is described. the shape. of \( f(x)=\sqrt{x} \), but shifted six units down and then reflected in both the \( x \)-axis and the \( y \)-axis \( g(x)=\square \)

To achieve the desired transformation, start with the original function \( f(x) = \sqrt{x} \). Shifting it down 6 units gives you \( f(x) - 6 = \sqrt{x} - 6 \). Reflecting in the \( x \)-axis changes the sign of the function, resulting in \( -(f(x) - 6) = -\sqrt{x} + 6 \). Finally, reflecting in the \( y \)-axis transforms the input as well, leading to \( g(x) = -\sqrt{-x} + 6 \). So, the final equation is \( g(x) = -\sqrt{-x} + 6 \).