Question

which equation represents the function graphed on the coordinate plane? \\(\bigcirc\\) \\(g(x) = |x + 1| + 3\\) \\(\bigcirc\\) \\(g(x) = |x + 3| - 1\\) \\(\bigcirc\\) \\(g(x) = |x - 1| + 3\\) \\(\bigcirc\\) \\(g(x) = |x + 3| + 1\\)

Explanation:

Step1: Recall absolute value vertex form

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

Step2: Identify the vertex from the graph

From the coordinate plane, the vertex of the V-shaped graph is at $(1, 3)$. So $h=1$ and $k=3$.

Step3: Substitute h and k into the form

Substitute $h=1$ and $k=3$ into $g(x) = |x - h| + k$:
$g(x) = |x - 1| + 3$

Step4: Match with given options

Compare the derived equation to the provided options; it matches the third option.

Answer:

g(x) = |x - 1| + 3