which interval contains a local minimum for the graphed function?\no -4, -2.5\no -2, -1\no 1, 2\no 2.5, 4

Answer:

The local minimum occurs where the function changes from decreasing to increasing. By observing the graph, the local - minimum is in the interval $[1,2]$. So the answer is C. $[1,2]$.

Explanation:

Step1: Understand local - minimum concept

A local minimum 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.

Step2: Analyze the graph

Examine the graph to find where the function changes from decreasing (going down as $x$ increases) to increasing (going up as $x$ increases).

Step3: Check the intervals

For the interval $[-4,-2.5]$, the function is increasing. For $[-2,-1]$, the function is decreasing. For $[1,2]$, the function has a local minimum as it changes from decreasing to increasing. For $[2.5,4]$, the function is increasing.