Given the function y=−x+4−−−−√

Question

, describe the transformations from the parent function y=x−−√
. Select all that apply.(1 point)
Responses

down 4 units
down 4 units

reflected over the y-axis
reflected over the y-axis

reflected over the x-axis
reflected over the x-axis

right 4 units
right 4 units

left 4 units
left 4 units

up 4 units

Answer 1

To analyze the function \( y = -\sqrt{x} + 4 \) and describe the transformations from the parent function \( y = \sqrt{x} \), let's break down the transformations.

1. Reflection Over the X-axis: The negative sign in front of the square root (\(-\sqrt{x}\)) indicates that the function is reflected over the x-axis.

2. Vertical Shift Upward: The \( +4 \) indicates that the entire function is shifted upward by 4 units.

So, the correct transformations from the parent function \( y = \sqrt{x} \) to \( y = -\sqrt{x} + 4 \) are:

• Reflected over the x-axis
• Up 4 units

The other options (down 4 units, reflected over the y-axis, right 4 units, left 4 units) do not apply to this transformation.

Thus, the selected transformations are:

• Reflected over the x-axis
• Up 4 units