which function is represented by the graph?\n$f(x)=-|x - 3|+4$\n$f(x)=-|x + 3|+4$\n$f(x)=-|x…
which function is represented by the graph?\n$f(x)=-|x - 3|+4$\n$f(x)=-|x + 3|+4$\n$f(x)=-|x - 4|+3$\n$f(x)=-|x + 4|+3$
Answer
Explanation:
Step1: Recall the vertex form of an absolute - value function
The vertex form of an absolute - value function is (y = a|x - h|+k), where ((h,k)) is the vertex of the graph.
Step2: Identify the vertex of the given graph
From the graph, the vertex of the absolute - value function is ((- 3,4)). So (h=-3) and (k = 4).
Step3: Substitute (h) and (k) into the vertex form
Substituting (h=-3) and (k = 4) into (y=a|x - h|+k), we get (y=a|x+3| + 4).
Step4: Determine the value of (a)
Since the graph opens downwards, (a=-1).
Answer:
(f(x)=-|x + 3|+4)