Question

over what interval is the graph of $y = |x + 6|$ decreasing?
a. $(-infty, -6)$
b. $(-infty, 6)$
c. $(-6, infty)$
d. $(6, infty)$

Explanation:

Step1: Identify vertex of absolute value

The vertex of $y=|x-h|$ is at $x=h$. For $y=|x+6|=|x-(-6)|$, vertex is at $x=-6$.

Step2: Analyze decreasing interval

Absolute value graphs open upward, so they decrease left of the vertex. The interval left of $x=-6$ is $(-\infty, -6)$.

Answer:

A. $(-\infty, -6)$