Question

use interval notation to write the interval(s) over which ( f ) is

a. increasing.

b. decreasing.

c. constant.

Explanation:

Step1: Identify the increasing interval

For a function \(y = f(x)\), it is increasing when as \(x\) increases, \(y\) also increases. Looking at the graph, we can see that the function is increasing in two intervals: from \(-\infty\) to \(-3\) and from \(-2\) to \(0\). In interval notation, these are \((-\infty,-3)\) and \((-2,0)\).

Step2: Identify the decreasing interval

The function is decreasing when as \(x\) increases, \(y\) decreases. From the graph, the function is decreasing in the interval \((0,3)\).

Step3: Identify the constant interval

The function is constant when as \(x\) increases, \(y\) remains the same. From the graph, the function is constant in the interval \((3,\infty)\).

Answer:

a. \((-\infty,-3)\cup(-2,0)\)
b. \((0,3)\)
c. \((3,\infty)\)