Question

which function is represented by this graph? options: \\( f(x)=|x + 1| - 2 \\), \\( f(x)=|x + 1| + 2 \\), \\( f(x)=|x - 1| - 2 \\), \\( f(x)=|x - 1| + 2 \\)

Explanation:

Step1: Recall absolute value form

The vertex form of an absolute value function is $f(x)=|x-h|+k$, where $(h,k)$ is the vertex of the V-shaped graph.

Step2: Identify the vertex

From the graph, the vertex (the lowest point of the V) is at $(1, 2)$. So $h=1$, $k=2$.

Step3: Substitute into the formula

Substitute $h=1$ and $k=2$ into $f(x)=|x-h|+k$:
$f(x)=|x-1|+2$

Answer:

$f(x)=|x-1|+2$ (matching the last option)