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

Explanation:

Step1: Analyze the absolute maximum

The function \(y = f(x)\) has no upper - bound as the graph goes upwards indefinitely (the right - hand side of the graph has no end). So, there is no absolute maximum.

Step2: Analyze the absolute minimum

Looking at the \(y\) - values of the function. The lowest point on the graph occurs at the point \((0,0)\). So, \(f(0)=0\) is the absolute minimum.

Answer:

For the absolute maximum: B. There is no absolute maximum for \(y = f(x)\)
For the absolute minimum: A. The absolute minimum of \(y = f(x)\) is \(f(0)=0\)