Question

the absolute - value function (f) has a range of ((-5,infty)), and a graph that is symmetric about the line (x = 4), and has a (y) - intercept of 1. identify the graph of (f).

Explanation:

Step1: Analyze range

The range of the function is $(- 5,\infty)$. This means the minimum - value of the function is $y=-5$.

Step2: Analyze axis of symmetry

The graph is symmetric about the line $x = 4$. So the vertex of the absolute - value function is on the line $x = 4$.

Step3: Analyze y - intercept

The y - intercept is 1, which means the function passes through the point $(0,1)$.

Answer:

The graph with a vertex at $(4, - 5)$ and passing through $(0,1)$ (the correct graph among the options which has a V - shape, vertex at $x = 4,y=-5$ and intersects the y - axis at $y = 1$). Since the options are not clearly labeled, you would need to check for a graph that meets these criteria: a V - shaped absolute - value graph with vertex at $(4,-5)$ and y - intercept of 1.