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.
(type integers or simplified fractions.)
c. there is no local minimum for ( y = f(x) ).
select the correct answer and, if necessary, fill in the answer boxes to complete your choice.
a. the absolute maximum of ( y = f(x) ) is ( f(1)=5 ).
(type integers or simplified fractions.)
b. there is no absolute maximum for ( y = f(x) ).
select the correct answer and, if necessary, fill in the answer boxes to complete your choice.
a. the absolute minimum of ( y = f(x) ) is ( f()= ).
(type integers or simplified fractions.)
b. there is no absolute minimum for ( y = f(x) ).

Explanation:

Step1: Identify absolute minimum

The absolute minimum of a function is the lowest \( y - \) value on its graph. Looking at the points \((1,5)\), \((2,3)\), \((3,4)\), \((4,1)\), the \( y - \) value \(1\) is the smallest. The \( x - \) value corresponding to \( y = 1\) is \(4\).

Answer:

A. The absolute minimum of \(y = f(x)\) is \(f(4)=1\)