To determine the function [tex]\( h(x) \)[/tex], let's analyze the transformation of the given parent function [tex]\( f(x) = \sqrt{x} \)[/tex].
1. Identify the Parent Function:
The given parent function is [tex]\( f(x) = \sqrt{x} \)[/tex], which is a basic square root function.
2. Understand the Transformation:
The transformation involves a horizontal shift. A horizontal shift of a function [tex]\( f(x) \)[/tex] is described generally as [tex]\( f(x - c) \)[/tex], where [tex]\( c \)[/tex] is the number of units of the shift.
- If [tex]\( c > 0 \)[/tex], the shift is to the right.
- If [tex]\( c < 0 \)[/tex], the shift is to the left.
3. Determine the Specific Shift:
The function [tex]\( h(x) = \sqrt{x - 4} \)[/tex] indicates a horizontal shift of 4 units to the right. This is because [tex]\( (x - 4) \)[/tex] means you take the input [tex]\( x \)[/tex] and shift everything 4 units to the right before applying the square root function.
Thus, the function [tex]\( h(x) \)[/tex] is obtained by horizontally shifting the parent function [tex]\( \sqrt{x} \)[/tex] 4 units to the right.
Therefore, the function [tex]\( h(x) \)[/tex] is:
[tex]\[
h(x) = \sqrt{x - 4}
\][/tex]
