Question

how does the graph of (y = \sqrt{x} + 2) compare to the graph of the parent square root function?

• the graph is a horizontal shift of the parent function 2 units right.
• the graph is a horizontal shift of the parent function 2 units left.
• the graph is a vertical shift of the parent function 2 units up.
• the graph is a vertical shift of the parent function 2 units down.

Explanation:

Identify the parent function and the given function

Using the Square Root Function Transformations knowledge point

$$
LATEXBLOCK0
$$

Analyze the transformation

Using the Vertical Translation knowledge point

$$
LATEXBLOCK1
$$

This represents a vertical shift of the parent function 2 units up.

Answer:

• The graph is a horizontal shift of the parent function 2 units right.
• The graph is a horizontal shift of the parent function 2 units left.
• The graph is a vertical shift of the parent function 2 units up. (Correct answer)
• The graph is a vertical shift of the parent function 2 units down.