Question

the given function ( f(x) ) is defined on the interval ( -9,9 ) and represented by the graph below. find the ( x ) - value(s) at which the absolute maximum value of ( f(x) ) occurs.

Explanation:

Step1: Understand the concept of absolute maximum

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

Step2: Analyze the graph

We look at the \(y -\)coordinates of the points on the graph of \(y = f(x)\) for \(x\in[-9,9]\). The highest \(y -\)value occurs at \(x = 9\) (by visually inspecting the graph, the point at \(x = 9\) has a higher \(y -\)coordinate compared to other candidate points such as the \(y -\)intercept and the left - hand endpoint).

Answer:

\(9\)