Question

f(x) = \sqrt{x + 2} what are the transformations of this function compared to the parent function? translated up 2 translated right 2 translated left 2 translated down 2

Explanation:

Step1: Recall parent function

The parent function of a square root function is \( y = \sqrt{x} \).

Step2: Analyze transformation rules

For a function of the form \( y=\sqrt{x + h} \), the horizontal translation rule is: if \( h>0 \), the graph is translated left \( h \) units; if \( h < 0 \), the graph is translated right \( |h| \) units.

In the given function \( f(x)=\sqrt{x + 2} \), we can rewrite it as \( y=\sqrt{x-(- 2)} \), here \( h=- 2\) (comparing with \( y=\sqrt{x + h}\), actually \( h = 2\) in the form \( y=\sqrt{x+h}\)). Since \( h = 2>0 \), according to the horizontal translation rule, the graph of \( f(x)=\sqrt{x + 2} \) is translated 2 units to the left compared to the parent function \( y=\sqrt{x} \).

Answer:

Translated left 2 (the option in the orange box)