which equation represents the function graphed on the coordinate plane?\n○ (g(x)=|x - 4|-10)\n○ (g(x)=|x +…

Explanation:

Step1: Recall vertex - form of absolute - value function

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

Step2: Identify the vertex of the graph

From the graph, the vertex of the absolute - value function is at the point $(4, - 10)$.

Step3: Substitute the vertex values into the general form

Substituting $h = 4$ and $k=-10$ into $y=a|x - h|+k$ (since $a = 1$ for the basic shape of the absolute - value function), we get $y=|x - 4|-10$.

Answer:

$g(x)=|x - 4|-10$