Use transformations to explain how the graph of \( f \) can be found by using the graph of \( y=\sqrt{x} \). \( f(x)=-\sqrt{x-2} \) Which of the following explains the transformations to find the graph of \( f \) ? Shifting of \( y=\sqrt{x} \) to the right 2 units and reflected about the \( x \)-axis. Shifting of \( y=\sqrt{x} \) to the left 2 units and reflected about the \( y \)-axis. Shifting of \( y=\sqrt{x} \) to the right 2 units and reflected about the \( y \)-axis. Shifting of \( y=\sqrt{x} \) to the left 2 units and reflected abo-it the \( x \)-axis.

To transform the graph of \( y = \sqrt{x} \) into the graph of \( f(x) = -\sqrt{x-2} \), we first shift the graph of \( y = \sqrt{x} \) to the right by 2 units. This is because of the \( (x-2) \) inside the square root, which moves our original function's starting point from \( (0,0) \) to \( (2,0) \). Next, the negative sign in front of the square root indicates a reflection over the \( x \)-axis, flipping the graph upside down. So, the correct explanation of the transformations is: shifting of \( y = \sqrt{x} \) to the right 2 units and reflected about the \( x \)-axis! This transformation creates a function that starts at the point \( (2,0) \) and goes downward from there.