which interval contains a local minimum for the graphed function? -4, -2.5 -2, -1 1, 2 2.5, 4

Explanation:

Step1: Recall local - minimum definition

A local minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze each interval

• For $[-4, - 2.5]$: The function is decreasing.
• For $[-2,-1]$: The function has a local minimum at approximately $x=-0.44$ where $y = - 4.3$. The function changes from decreasing to increasing in this interval.
• For $[1,2]$: The function is increasing.
• For $[2.5,4]$: The function is decreasing then increasing but the local - minimum in this region is at $x = 3$ which is not fully within the interval $[2.5,4]$.

Answer:

$[-2,-1]$