Question

use the graph of a function ( y = f(x) ) to find the absolute maximum and the absolute minimum, if they exist. identify any local maximum values or local minimum values.
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. the absolute maximum is
(type an integer or a simplified fraction.)
b. there is no absolute maximum for ( y = f(x) ).

Explanation:

Step1: Understand the concept of absolute maximum

The absolute maximum of a function \(y = f(x)\) on its domain is the largest \(y -\)value that the function attains.

Step2: Analyze the given points on the graph

Looking at the points \((-2,-2)\), \((-1, - 4)\), \((3,0)\), \((5,3)\), \((7,2)\). The \(y -\)values are \(y=-2\), \(y = - 4\), \(y = 0\), \(y=3\), \(y = 2\).

Step3: Compare the \(y -\)values

By comparing the values \(3>2>0>-2>-4\)

Answer:

A. The absolute maximum is \(3\)