which equation represents the function graphed on the coordinate plane?\n○ (g(x)=|x + 4|-2)\n○ (g(x)=|x…

Answer:

$g(x)=|x + 4|-2$

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

The vertex of the given graph is at the point $(-4,-2)$.

Step3: Substitute vertex values into the general form

Substituting $h=-4$ and $k = - 2$ into $y=a|x - h|+k$ (assuming $a = 1$ since there is no vertical stretch or compression), we get $y=|x-(-4)|-2=|x + 4|-2$. So the function is $g(x)=|x + 4|-2$.