Question

how does the graph of $y = \sqrt{x} + 2$ compare to the graph of the parent square root function?\
\bigcirc the graph is a horizontal shift of the parent function 2 units right.\
\bigcirc the graph is a horizontal shift of the parent function 2 units left.\
\bigcirc the graph is a vertical shift of the parent function 2 units up.\
\bigcirc the graph is a vertical shift of the parent function 2 units down.

Explanation:

The parent square root function is \( y = \sqrt{x} \). For a function of the form \( y = f(x)+k \), if \( k>0 \), the graph of \( y = f(x) \) is shifted vertically up by \( k \) units; if \( k < 0 \), it is shifted vertically down by \( |k| \) units. In the function \( y=\sqrt{x}+2 \), we have \( f(x)=\sqrt{x} \) and \( k = 2>0 \), so it is a vertical shift of the parent function 2 units up. Horizontal shifts are of the form \( y=f(x - h) \), which is not the case here.

Answer:

The graph is a vertical shift of the parent function 2 units up.