Sure, let's go through the process of shifting the graph of the function [tex]\( y = \sqrt{x} \)[/tex] to the right by 3 units.
1. Understand the Original Function:
The given function is [tex]\( y = \sqrt{x} \)[/tex]. This is the graph of the square root function.
2. Shifting the Function Horizontally:
To shift a function horizontally, you modify the argument of the function. Specifically, to shift it to the right by [tex]\( h \)[/tex] units, you replace [tex]\( x \)[/tex] with [tex]\( x-h \)[/tex]. In this case, [tex]\( h = 3 \)[/tex].
3. Apply the Shift:
Replace [tex]\( x \)[/tex] with [tex]\( x-3 \)[/tex] in the original function. Therefore, the new function becomes:
[tex]\[
y = \sqrt{x - 3}
\][/tex]
This transformation modifies the original function [tex]\( y = \sqrt{x} \)[/tex] so that the graph is shifted to the right by 3 units.
So, the function whose graph is the graph of [tex]\( y = \sqrt{x} \)[/tex], but shifted to the right by 3 units, is:
[tex]\[
y = \sqrt{x - 3}
\][/tex]
This is the simplified and final form of the function.
