The problem asks us to determine the intervals on which the given function is increasing and decreasing. We need to look at the graph and identify where the function's $y$-values are increasing as $x$ increases, and where the $y$-values are decreasing as $x$ increases.

1. Problem Description

The problem asks us to determine the intervals on which the given function is increasing and decreasing. We need to look at the graph and identify where the function's $y$-values are increasing as $x$ increases, and where the $y$-values are decreasing as $x$ increases.

2. Solution Steps

First, we identify the points where the function changes direction. These points are approximately at $x=-3$ and $x=1$.

The function is increasing when its slope is positive. Looking at the graph, this occurs to the left of $x=-3$ and to the right of $x=1$. Therefore, the function is increasing on the intervals $(-\infty, -3)$ and $(1, \infty)$.

The function is decreasing when its slope is negative. Looking at the graph, this occurs between $x=-3$ and $x=1$. Therefore, the function is decreasing on the interval $(-3, 1)$.

3. Final Answer

Increasing on the interval(s): $(-\infty, -3), (1, \infty)$

Decreasing on the interval(s): $(-3, 1)$