which graph represents the function f(x) = |x + 3|?

Explanation:

Step1: Recall the form of absolute - value function

The general form of an absolute - value function is (y = |x - h|+k), and its graph is a V - shaped graph. For the function (f(x)=|x + 3|), we can rewrite it as (f(x)=|x-(- 3)|), where (h=-3) and (k = 0).

Step2: Find the vertex of the function

The vertex of the absolute - value function (y = |x - h|+k) is at the point ((h,k)). For (y = |x + 3|), the vertex is at the point ((-3,0)). When (x=-3), (y = |-3 + 3|=0).

Step3: Analyze the behavior of the function for (x\gt - 3) and (x\lt - 3)

When (x\gt - 3), say (x=-2), then (f(-2)=|-2 + 3|=1). The function (y=x + 3) for (x\geq - 3). When (x\lt - 3), say (x=-4), then (f(-4)=|-4 + 3|=1). The function (y=-(x + 3)=-x - 3) for (x\lt - 3). The graph with the vertex at ((-3,0)) and opening upwards is the correct graph for (y = |x + 3|).

Answer:

The graph with the vertex at the point ((-3,0)) and opening upwards. (Since no specific option is labeled, this is a general description of the correct graph. If there were options labeled A, B, etc., we would identify the option with the vertex at ((-3,0)) and a V - shape opening upwards).