Question

the graph of an absolute value function, h(x), is shown below
select the function below that correctly represents the function of the graph.
a. ( y = -|x - 6| + 4 )
b. ( y = -|x + 6| + 4 )
c. ( y = |x - 6| + 4 )
( y = |x + 6| + 4 )

Explanation:

Step1: Recall absolute value vertex form

The general 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

From the graph, the vertex (the peak of the V - shaped graph) is at \((-6, 4)\). So \( h=-6 \) and \( k = 4 \).

Step3: Determine the direction (a - value)

The graph opens downward, which means the coefficient \( a \) of the absolute value term is negative (\( a<0 \)).

Step4: Substitute h, k, and a into the formula

Substituting \( h=-6 \), \( k = 4 \), and \( a=-1 \) into \( y=a|x - h|+k \), we get \( y=-|x - (-6)|+4=-|x + 6|+4 \).

Answer:

B. \( y = -|x + 6|+4 \)