Question

which interval by the graphed function contains a local minimum? -5, -3, -1, 1, 1, 3, -3, -1

Explanation:

Step1: Recall local - minimum definition

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

Step2: Analyze the intervals

We need to check each interval to see if there is a local - minimum within it.
For the interval \([-5,-3]\): The function is increasing on this interval, so there is no local minimum.
For the interval \([-1,1]\): The function is decreasing then increasing, and there is a local minimum in this interval.
For the interval \([1,3]\): The function is decreasing on this interval, so there is no local minimum.
For the interval \([3,5]\): The function is increasing on this interval, so there is no local minimum.

Answer:

\([-1,1]\)