Given:
The graph of a function.
To find:
The intervals where the function is increasing and decreasing.
Solution:
A function is increasing if the function increases as the value of x increases.
A function is decreasing if the function decreases as the value of x increases.
From the given graph it is clear that the graph is decreasing for [tex]x<-2[/tex], then the graph increasing for [tex]-2<x<2[/tex] after that the function again start decreasing for [tex]x>2[/tex].
Function Increasing over: [tex](\infty,-2)\cup (2,\infty)[/tex]
Function decreasing over: [tex](-2,2)[/tex].
Therefore, the function is increasing over the interval [tex](\infty,-2)\cup (2,\infty)[/tex] and the function is decreasing over the interval [tex](-2,2)[/tex].