Answer :
Step-by-step explanation:
To find points on the graph of the reflection of [tex]\( f(x) = \sqrt{x} \)[/tex] over the y-axis, we need to reflect the function. Reflecting a function over the y-axis involves replacing [tex]\( x \) with \( -x \)[/tex] in the function's equation. So, the reflected function will be:
[tex]\[ f(x) = \sqrt{-x} \][/tex]
However, [tex]\(\sqrt{-x}\)[/tex] is only defined for [tex]\(x \leq 0\)[/tex], since the square root function requires a non-negative argument.
Here are some points that lie on the graph of the reflected function [tex]\( f(x) = \sqrt{-x} \)[/tex]
1. For [tex]\( x = -1 \):[/tex]
[tex]\[ f(-1) = \sqrt{-(-1)} = \sqrt{1} = 1 \][/tex]
Point: (-1, 1)
2. For [tex]\( x = -4 \):[/tex]
[tex]\[ f(-4) = \sqrt{-(-4)} = \sqrt{4} = 2 \][/tex]
Point: (-4, 2)
3. For [tex]\( x = 0 \):[/tex]
[tex]\[ f(0) = \sqrt{-0} = \sqrt{0} = 0 \][/tex]
Point: (0, 0)
So, one possible list of points that lie on the graph of the reflection is [tex]\((-1, 1)\), \((-4, 2)\), and \((0, 0)\).[/tex]
If you have access to a graphing calculator, you can verify these points by graphing the function [tex]\( f(x) = \sqrt{-x} \).[/tex]
