identify the extrema of the graph.

Answer

Explanation:

Step1: Understand the definitions

Absolute maximum: The highest point on the entire graph.
Absolute minimum: The lowest point on the entire graph.
Relative maximum: A point that is higher than the neighboring points.
Relative minimum: A point that is lower than the neighboring points.

Step2: Analyze each point

Point A: It is a local high - point (higher than its immediate neighbors), so it is a relative maximum.
Point B: It is a local low - point (lower than its immediate neighbors), so it is a relative minimum.
Point C: It is the lowest point on the entire graph shown, so it is the absolute minimum.
Point D: It is a local high - point (higher than its immediate neighbors), but not the highest on the entire graph.

Answer:

Absolute Minimum: Point C
Absolute Maximum: There is none (as the graph may extend further down on the left and we are only given a part of the graph, but within the visible part, the highest (y) - value is at point A, but if we consider the domain of the function as the given graph, and since the left - hand side of the graph goes down infinitely (assuming the function is defined for (x\lt - 3) as per the axis labels), there is no absolute maximum. If we assume the domain is the (x) - values from the left - most point (where the graph starts rising) to (x = 4), still point A is not an absolute maximum as the function could have higher values outside the visible window. But if we consider the given plotted points, and assume the domain is the (x) - values for which the function is plotted (from the left - most point to (x = 4)), since the left - hand side of the graph (for (x\lt - 3)) is going down, and within the plotted (x) - range ((x) from left - most to (x = 4)), the (y) - value at point A is higher than other non - infinite (y) - values. But in a strict calculus sense (if the function is defined for all real (x) where it is graphed), since the left - hand side goes down infinitely, there is no absolute maximum. If we consider the finite (x) range of the plotted graph (say from (x=-3) to (x = 4)), point A is a relative maximum. But generally, for the given graph (assuming the function is defined as (y = f(x)) for (x) in the visible (x) - axis range), there is no absolute maximum.
Relative Minimum: Point B
Relative Maximum: Point A