which graph represents the function g(x) = |x + 4| + 2?

Explanation:

Step1: Recall the parent - function of absolute - value

The parent function of an absolute - value function is (y = |x|), which has a vertex at ((0,0)) and is in the shape of a "V".

Step2: Analyze the transformation of (y = |x|) to (y=|x + 4|+2)

For the function (y = |x + 4|+2), the transformation (x\to x + 4) shifts the graph of (y = |x|) 4 units to the left. The transformation (y\to y - 2) (or adding 2 to the right - hand side) shifts the graph 2 units up. The vertex of the function (y = |x|) is ((0,0)). After the transformation (x\to x + 4) and (y\to y+2), the vertex of (y = |x + 4|+2) is ((-4,2)).

Answer:

The graph with the vertex at the point ((-4,2)) represents the function (g(x)=|x + 4|+2). Without specific labels on the given graphs, you should look for the graph where the "V" shape has its lowest point (vertex) at (x=-4) and (y = 2).