To determine how the graph of [tex]\( y = \sqrt{x} + 2 \)[/tex] compares to the graph of the parent square root function [tex]\( y = \sqrt{x} \)[/tex], let's examine the given function step by step:
1. Identify the Parent Function:
The parent function is [tex]\( y = \sqrt{x} \)[/tex]. This is the basic square root function, whose graph starts at the origin (0,0) and increases slowly as [tex]\( x \)[/tex] increases.
2. Analyze the Transformation:
In the function [tex]\( y = \sqrt{x} + 2 \)[/tex], we observe that there is an additional "+2" outside the square root.
3. Understand the Effect of the Transformation:
- Adding a constant outside the function [tex]\( \sqrt{x} \)[/tex] results in a vertical shift.
- Specifically, [tex]\( y = \sqrt{x} + 2 \)[/tex] means that every output value of [tex]\( y \)[/tex] from the parent function [tex]\( y = \sqrt{x} \)[/tex] has been increased by 2 units.
4. Conclude the Transformation:
- Therefore, the graph of [tex]\( y = \sqrt{x} + 2 \)[/tex] is the graph of [tex]\( y = \sqrt{x} \)[/tex] shifted upward by 2 units.
Based on this analysis, the correct answer is:
The graph of [tex]\( y = \sqrt{x} + 2 \)[/tex] is a vertical shift of the parent function 2 units up.
Thus, the best option is:
The graph is a vertical shift of the parent function 2 units up.
