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If you horizontally shift the square root parent function, [tex][tex]$F(x)=\sqrt{x}$[/tex][/tex], right eight units, what is the equation of the new function?

Sagot :

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.