Question

which of the following is the graph of this absolute value function?
$y = |x - 3|$

Explanation:

Step1: Identify vertex of absolute value

The vertex of $y=|x-h|$ is at $(h, 0)$. For $y=|x-3|$, $h=3$, so vertex is $(3, 0)$.

Step2: Verify key points

When $x=0$, $y=|0-3|=3$, so the point $(0,3)$ is on the graph.

Step3: Match to given graphs

Check which graph has vertex $(3,0)$ and passes through $(0,3)$.

Answer:

The first graph (leftmost graph with vertex at (3, 0) and passing through (0, 3))