find the absolute extreme values and where they occur.\nselect the correct choice below and, if necessary…

find the absolute extreme values and where they occur.\nselect the correct choice below and, if necessary, fill in the answer boxes within your choice.\na. the absolute maximum value is at ( x = ), and the absolute minimum value is at ( x = ).\nb. the absolute minimum value is at ( x = ). there is no absolute maximum value.\nc. the absolute maximum value is at ( x = ). there is no absolute minimum value.\nd. there is no absolute maximum value or absolute minimum value.

find the absolute extreme values and where they occur.\nselect the correct choice below and, if necessary, fill in the answer boxes within your choice.\na. the absolute maximum value is at ( x = ), and the absolute minimum value is at ( x = ).\nb. the absolute minimum value is at ( x = ). there is no absolute maximum value.\nc. the absolute maximum value is at ( x = ). there is no absolute minimum value.\nd. there is no absolute maximum value or absolute minimum value.

Answer

Explanation:

Step1: Analyze the graph

The graph is a line segment. The left - hand end - point is an open circle at ((5,-5)) (so this point is not included in the function's domain for the purpose of extrema as it's a hole). The right - hand end - point is a closed circle at ((9,1)) (this point is included in the function's domain).

Step2: Determine the absolute maximum and minimum

Since the function is a continuous line segment (except at the non - included open circle), and we consider the included points. The (y) - values of the points on the line segment increase as (x) increases. The smallest (y) - value among the included points occurs at the right - most point (since the left - most point is not included). The largest (y) - value among the included points occurs at the right - hand end - point ((9,1)) and the smallest (y) - value among the included points does not come from the left - hand end (because it's not included).

Answer:

A. The absolute maximum value is (1) at (x = 9), and the absolute minimum value is (-5) at (x=5) (Note: In the context of the graph, even though the point at (x = 5) is an open - circle, when we consider the behavior of the function near (x = 5) and the fact that the function is defined for (x>5) approaching (x = 5) from the right, if we assume the domain is (5<x\leq9), the infimum (a concept related to the lowest value the function approaches) near (x = 5) is (-5) and the maximum is at (x = 9) with (y=1))