Answer :
To determine the new function when the square root parent function [tex]\( F(x) = \sqrt{x} \)[/tex] is shifted to the right by eight units, we need to understand how horizontal shifts affect a function.
For a general function [tex]\( f(x) \)[/tex], a horizontal shift to the right by [tex]\( h \)[/tex] units is represented by [tex]\( f(x - h) \)[/tex]. In this case, [tex]\( h \)[/tex] is positive because we are shifting to the right.
Given that [tex]\( F(x) = \sqrt{x} \)[/tex], if we shift this function to the right by 8 units, we replace [tex]\( x \)[/tex] with [tex]\( x - 8 \)[/tex] in the function. Thus, the new function [tex]\( G(x) \)[/tex] becomes:
[tex]\[ G(x) = \sqrt{x - 8} \][/tex]
Now, let's compare this with the options provided:
A. [tex]\( G(x) = \sqrt{x - 8} \)[/tex]
B. [tex]\( G(x) = \sqrt{x + 8} \)[/tex]
C. [tex]\( G(x) = \sqrt{x} - 8 \)[/tex]
D. [tex]\( G(x) = \sqrt{x} + 8 \)[/tex]
The correct equation for the new function after shifting [tex]\( \sqrt{x} \)[/tex] eight units to the right is:
A. [tex]\( G(x) = \sqrt{x - 8} \)[/tex]
Therefore, the answer is [tex]\(\boxed{A}\)[/tex].
For a general function [tex]\( f(x) \)[/tex], a horizontal shift to the right by [tex]\( h \)[/tex] units is represented by [tex]\( f(x - h) \)[/tex]. In this case, [tex]\( h \)[/tex] is positive because we are shifting to the right.
Given that [tex]\( F(x) = \sqrt{x} \)[/tex], if we shift this function to the right by 8 units, we replace [tex]\( x \)[/tex] with [tex]\( x - 8 \)[/tex] in the function. Thus, the new function [tex]\( G(x) \)[/tex] becomes:
[tex]\[ G(x) = \sqrt{x - 8} \][/tex]
Now, let's compare this with the options provided:
A. [tex]\( G(x) = \sqrt{x - 8} \)[/tex]
B. [tex]\( G(x) = \sqrt{x + 8} \)[/tex]
C. [tex]\( G(x) = \sqrt{x} - 8 \)[/tex]
D. [tex]\( G(x) = \sqrt{x} + 8 \)[/tex]
The correct equation for the new function after shifting [tex]\( \sqrt{x} \)[/tex] eight units to the right is:
A. [tex]\( G(x) = \sqrt{x - 8} \)[/tex]
Therefore, the answer is [tex]\(\boxed{A}\)[/tex].
