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: Recall the definition of absolute maximum

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

Step2: Analyze the given points on the graph

We are given the points \((-2,-2)\), \((-1, - 4)\), \((3,0)\), \((5,3)\), \((7,2)\). Comparing the \(y -\)values: \(-4<-2 <0<2<3\)

Answer:

A. The absolute maximum is \(3\)