Question

here is a graph of the function g. use the graph to find the following. if there is more than one answer, separate them with commas. all local maximum values of g: all values at which g has a local maximum:

Explanation:

Step1: Recall local - maximum definition

A local maximum of a function is a point where the function value is greater than or equal to the values at nearby points.

Step2: Identify local - maximum points on the graph

By observing the graph of \(y = g(x)\), we look for the peaks. The function \(y = g(x)\) has local maxima at \(x=-2\) and \(x = 1\). The value of the function at \(x=-2\) is \(y = 0\) and at \(x = 1\) is \(y=3\).

Answer:

All local maximum values of \(g\): \(0,3\)
All values at which \(g\) has a local maximum: \(-2,1\)