Question

determine the intervals on which the function is increasing, decreasing, and constant. list the interval(s) on which the function is increasing. (type your answer in interval notation. use a comma to separate answers as needed.)

Explanation:

Step1: Recall the definition of an increasing function

A function \(y = f(x)\) is increasing on an interval if, for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the given graph

Looking at the graph:

• For the left - hand part of the graph (before the local maximum), we observe that as \(x\) increases from \(-\infty\) to \(- 8\), the \(y\) - values of the function increase.
• For the right - hand part of the graph (after the local minimum), as \(x\) increases from \(0\) to \(2\), the \(y\) - values of the function increase.

In interval notation, the intervals where the function is increasing are \((-\infty,-8)\) and \((0,2)\)

Answer:

\((-\infty,-8),(0,2)\)