which graph represents the function f(x) = -|x + 3|?
which graph represents the function f(x) = -|x + 3|?
Answer
Answer:
The first graph (top - left graph)
Explanation:
Step1: Analyze the vertex
For the absolute - value function (y = a|x - h|+k), in the function (f(x)=-|x + 3|), we have (h=-3) and (k = 0). So the vertex of the graph is at the point ((-3,0)).
Step2: Analyze the slope
The coefficient (a=-1). When (x\lt - 3), (f(x)=-( - (x + 3))=x + 3), and the slope is (1). When (x\geq - 3), (f(x)=-(x + 3)=-x - 3), and the slope is (-1). The first graph has a vertex at ((-3,0)) and the correct slopes for the two parts of the absolute - value function.