how does the graph of $y = sqrt{x}+2$ compare to the graph of the parent square root function?\nthe graph is…

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

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

Answer

Answer:

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

Explanation:

Step1: Recall parent - square root function

The parent square - root function is $y = \sqrt{x}$.

Step2: Analyze the transformation

For a function $y=f(x)+k$, when $k>0$, the graph of $y = f(x)$ is shifted vertically upwards by $k$ units. In the function $y=\sqrt{x}+2$, compared to $y = \sqrt{x}$, we have $k = 2$. So the graph of $y=\sqrt{x}+2$ is a vertical shift of the graph of $y=\sqrt{x}$ 2 units up.