Question

answer for the following questions about the graph below. answer in interval notation. answer dne if the interval does not exist.
a. in what interval(s) is the function is increasing?
b. in what interval(s) is the function is decreasing?

Explanation:

Step1: Recall the definition of increasing and decreasing functions

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 graph for increasing intervals

Looking at the graph, from \(x=-2\) to \(x = 0\), as \(x\) increases, \(y\) increases. Also, from \(x = 2\) to \(+\infty\), as \(x\) increases, \(y\) increases. In interval notation, the increasing intervals are \((-2,0)\cup(2,\infty)\).

Step3: Analyze the graph for decreasing intervals

Looking at the graph, from \(-\infty\) to \(x=-2\), as \(x\) increases, \(y\) decreases. Also, from \(x = 0\) to \(x=2\), as \(x\) increases, \(y\) decreases. In interval notation, the decreasing intervals are \((-\infty,-2)\cup(0,2)\).

Answer:

a. \((-2,0)\cup(2,\infty)\)
b. \((-\infty,-2)\cup(0,2)\)