Question

which of the following is the graph of this absolute value function?
$y = |x + 4|$

Explanation:

Step1: Identify parent function

The parent absolute value function is $y=|x|$, whose vertex is at $(0,0)$.

Step2: Analyze horizontal shift

For $y=|x+h|$, the graph shifts left by $h$ units. Here $h=4$, so shift $y=|x|$ left 4 units. The new vertex is at $(-4,0)$.

Step3: Match with given graphs

Check which graph has vertex at $(-4,0)$ and the V-shape of absolute value function.

Answer:

The middle graph (with vertex at $(-4, 0)$, rising on both sides of the vertex)