Question

the graph of $f(x) = -|x + 2|$ is a reflection across the select choice in relation to the parent function.

Explanation:

Step1: Recall Parent Function

The parent function of absolute value is \( y = |x| \), which opens upwards (vertex at origin, symmetric about \( y \)-axis).

Step2: Analyze Transformation

For \( f(x) = -|x + 2| \), the negative sign in front of the absolute value function reflects the graph of \( y = |x + 2| \) (which is a horizontal shift of parent \( y = |x| \)) across the \( x \)-axis. The horizontal shift (\( x + 2 \)) moves it left, but the reflection is due to the negative coefficient on the absolute value, which flips it over the \( x \)-axis.

Answer:

\( x \)-axis