Answer :
To determine the equation of the new function after horizontally shifting the square root function [tex]$F(x) = \sqrt{x}$[/tex] to the right by eight units, we need to understand how horizontal shifts affect the equation of a function.
1. Parent Function:
The original or parent function is [tex]$F(x) = \sqrt{x}$[/tex].
2. Horizontal Shift:
A horizontal shift involves moving the graph of the function left or right along the x-axis. If we want to shift the function to the right by a certain number of units, we need to replace [tex]$x$[/tex] with [tex]$(x - h)$[/tex], where [tex]$h$[/tex] is the number of units we want to shift.
3. Shift Right by 8 Units:
If we want to shift the graph to the right by 8 units, we need to replace [tex]$x$[/tex] with [tex]$(x - 8)$[/tex]. This means our new function will be [tex]$F(x - 8)$[/tex].
4. Substitute and Simplify:
Substituting [tex]$(x - 8)$[/tex] into the original function, we get:
[tex]\[ F(x - 8) = \sqrt{x - 8} \][/tex]
Thus, the equation of the new function after shifting the square root function [tex]$F(x) = \sqrt{x}$[/tex] to the right by eight units is:
[tex]\[ F(x) = \sqrt{x - 8} \][/tex]
This new expression, [tex]$F(x) = \sqrt{x - 8}$[/tex], represents the horizontally shifted square root function.
1. Parent Function:
The original or parent function is [tex]$F(x) = \sqrt{x}$[/tex].
2. Horizontal Shift:
A horizontal shift involves moving the graph of the function left or right along the x-axis. If we want to shift the function to the right by a certain number of units, we need to replace [tex]$x$[/tex] with [tex]$(x - h)$[/tex], where [tex]$h$[/tex] is the number of units we want to shift.
3. Shift Right by 8 Units:
If we want to shift the graph to the right by 8 units, we need to replace [tex]$x$[/tex] with [tex]$(x - 8)$[/tex]. This means our new function will be [tex]$F(x - 8)$[/tex].
4. Substitute and Simplify:
Substituting [tex]$(x - 8)$[/tex] into the original function, we get:
[tex]\[ F(x - 8) = \sqrt{x - 8} \][/tex]
Thus, the equation of the new function after shifting the square root function [tex]$F(x) = \sqrt{x}$[/tex] to the right by eight units is:
[tex]\[ F(x) = \sqrt{x - 8} \][/tex]
This new expression, [tex]$F(x) = \sqrt{x - 8}$[/tex], represents the horizontally shifted square root function.
