Question

f(x) = -√x
describe the transformation.
up 1
down 1
reflect over y-axis
reflect over x-axis

Explanation:

The parent function is \( y = \sqrt{x} \). For the function \( f(x)=-\sqrt{x} \), the negative sign in front of the square root indicates a reflection. A reflection over the x - axis is given by the transformation \( y=-f(x) \) when the original function is \( y = f(x) \). Here, if we take \( f(x)=\sqrt{x} \), then \( -f(x)=-\sqrt{x} \), which is a reflection over the x - axis. The options "Up 1" and "Down 1" would involve adding or subtracting 1 from the function (like \( y=\sqrt{x}+1 \) or \( y=\sqrt{x}-1 \)), which is not the case here. A reflection over the y - axis would be \( y = f(-x)=\sqrt{-x} \), which is not our function.

Answer:

D. Reflect over x - axis