Question

use the graph of ( y = f(x) ) to answer the questions. complete parts a through j.

f. what is/are the ( x )-intercept(s) of ( f )?
the ( x )-intercept(s) is/are ( x = ) (use a comma to separate answers as needed.)

Explanation:

Step1: Identify relative maxima

A relative maximum is a point where the function changes from increasing to decreasing. Looking at the graph, there are two such points: at \(x = - 2\) and \(x = 2\). The \(y\) - values (the maximum values) at these points are \(y = 4\) for both.

Step2: Determine \(x\) - intercepts

The \(x\) - intercepts are the points where \(y=f(x)=0\). From the graph, we can see that the function crosses the \(x\) - axis at \(x=-3\) and \(x = 3\).

Answer:

For the relative maxima: B. There are two relative maxima. The leftmost maximum is \(4\), and it occurs at \(x=-2\). The rightmost maximum is \(4\), and it occurs at \(x = 2\).
For the \(x\) - intercepts: The \(x\) - intercept(s) is/are \(x=-3,3\)