the graph shows the function f(x) = |x - h| + k. what is the value of k?\no k = -2.5\no k = -1\no k = 1\no k…

Explanation:

Step1: Recall vertex - form property

The vertex of the absolute - value function (y = |x - h|+k) is ((h,k)).

Step2: Identify the vertex from the graph

From the graph of (y = |x - h|+k), the vertex is the lowest point of the V - shaped graph. The vertex of the given graph is at the point ((2,- 2.5)).

Step3: Determine the value of (k)

In the vertex ((h,k)), the (y) - coordinate of the vertex gives the value of (k). Since the (y) - coordinate of the vertex ((2,-2.5)) is (-2.5), then (k=-2.5).

Answer:

(k = - 2.5)