Question

question 10 consider the function graphed at right. the function has a select an answer of at x = the function is increasing on the interval(s): the function is decreasing on the interval(s): question help: video message instructor post to forum

Explanation:

Step1: Identify the maximum/minimum

By observing the graph, the function has a peak (maximum). The x - coordinate of the peak is at \(x=- 2\) and the y - value at that point is \(y = 3\). So the function has a maximum of \(3\) at \(x=-2\).

Step2: Determine the increasing intervals

A function is increasing when the graph goes up as we move from left to right. From the graph, the function is increasing on the interval \((-\infty,-2)\).

Step3: Determine the decreasing intervals

A function is decreasing when the graph goes down as we move from left to right. From the graph, the function is decreasing on the interval \((-2,\infty)\).

Answer:

The function has a maximum of \(3\) at \(x = - 2\).
The function is increasing on the interval \((-\infty,-2)\).
The function is decreasing on the interval \((-2,\infty)\).