To horizontally shift the square root parent function [tex]\( F(x) = \sqrt{x} \)[/tex] to the right by eight units, we need to adjust the input variable [tex]\( x \)[/tex] in the function.
Here is the step-by-step explanation:
1. Understand Horizontal Shifts:
Horizontal shifts are transformations that move the graph of a function left or right. When shifting to the right, we subtract a constant from the input variable [tex]\( x \)[/tex]. Conversely, shifting to the left requires adding a constant to [tex]\( x \)[/tex].
2. Original Function:
The original function is [tex]\( F(x) = \sqrt{x} \)[/tex].
3. Applying the Shift:
To shift the function to the right by 8 units, we substitute [tex]\( x-8 \)[/tex] for [tex]\( x \)[/tex] in the original function. This means wherever we see [tex]\( x \)[/tex] in the function, we replace it with [tex]\( x-8 \)[/tex].
4. New Function:
By substituting [tex]\( x-8 \)[/tex] for [tex]\( x \)[/tex] in [tex]\( F(x) = \sqrt{x} \)[/tex], we get:
[tex]\[
G(x) = \sqrt{x - 8}
\][/tex]
Therefore, the correct equation for the new function after shifting the original function right by eight units is [tex]\( G(x) = \sqrt{x - 8} \)[/tex].
Hence, the answer is:
D. [tex]\( G(x) = \sqrt{x - 8} \)[/tex]
