use the graph to find the following. if there is more than one answer, separate them with commas. all values…

Explanation:

Step1: Recall local - minimum definition

A local minimum of a function (y = f(x)) is a point where the function value is less than or equal to the values of the function in a small open - interval around that point. Visually, on a graph, it is a "valley" point.

Step2: Examine the graph

Looking at the given graph of the function (y = f(x)), we identify the points where the function has local minima.

Answer:

From the graph, the (x) - values at which (f) has local minima are (x=- 4,x = 3). The local minimum values of (f) are the (y) - values at these points. The local minimum value at (x=-4) is (y = - 3) and the local minimum value at (x = 3) is (y=-1). So the local minimum values of (f) are (-3,-1) and the values of (x) at which (f) has local minima are (-4,3).