use interval notation to write the interval(s) over which (f) is (a) increasing, (b) decreasing, and (c)…

use interval notation to write the interval(s) over which (f) is (a) increasing, (b) decreasing, and (c) constant. if there is more than one interval, separate them with commas.

use interval notation to write the interval(s) over which (f) is (a) increasing, (b) decreasing, and (c) constant. if there is more than one interval, separate them with commas.

Answer

Explanation:

Step1: Identify increasing interval

An increasing function has a positive - slope. Looking at the graph, there is no interval where the function is increasing. So the increasing interval is the empty set, denoted as $\varnothing$.

Step2: Identify decreasing intervals

A decreasing function has a negative - slope. The function is decreasing on $(-\infty,-1)$ and $(2,\infty)$.

Step3: Identify constant interval

A constant function has a slope of 0. The function is constant on $[-1,2]$.

Answer:

(a) $\varnothing$ (b) $(-\infty,-1),(2,\infty)$ (c) $[-1,2]$