To compare the graph of [tex]\( y = \sqrt{x} + 2 \)[/tex] to the graph of the parent square root function [tex]\( y = \sqrt{x} \)[/tex], we need to analyze the transformations applied to the parent function.
1. Parent Function: The parent function is [tex]\( y = \sqrt{x} \)[/tex]. This function produces a curve starting at the origin (0, 0) and moving upwards to the right.
2. Transformation: The given function is [tex]\( y = \sqrt{x} + 2 \)[/tex]. Here, [tex]\( +2 \)[/tex] is added to the parent function [tex]\( \sqrt{x} \)[/tex].
In graphical transformations, adding a constant value outside of the function (i.e., [tex]\( y = f(x) + k \)[/tex]) results in a vertical shift of the graph. Specifically, the graph is shifted upwards by [tex]\( k \)[/tex] units if [tex]\( k \)[/tex] is positive.
- In [tex]\( y = \sqrt{x} + 2 \)[/tex], the [tex]\( +2 \)[/tex] indicates that every point on [tex]\( y = \sqrt{x} \)[/tex] will be shifted 2 units upwards.
Therefore, the correct description is:
- The graph is a vertical shift of the parent function 2 units up.
Hence, the correct answer is:
- The graph is a vertical shift of the parent function 2 units up.
