Question

find the absolute maximum and minimum for the given graph.
absolute maximum:
absolute minimum:

Explanation:

Step1: Understand the concept of absolute maximum and minimum

The absolute maximum of a function on an interval is the largest \(y -\)value (output) of the function on that interval. The absolute minimum is the smallest \(y -\)value (output) of the function on that interval.

Step2: Identify the \(y -\)coordinates of the key points

Looking at the graph, we have two key points (the endpoints or critical - like points in the context of the graph shown). One point has coordinates \((-4, - 3)\) and another has coordinates \((0,-2)\).
The \(y -\)coordinate of the first point is \(-3\) and the \(y -\)coordinate of the second point is \(-2\). Since \(-2>-3\) (because on the number line, \(-2\) is to the right of \(-3\)).

Answer:

Absolute maximum: \(-2\), Absolute minimum: \(-3\)