From the image, the graph is a continuous curve with alternating increasing and decreasing sections. Let's break this down:

1. Range:

The range of a function refers to all the possible values of $y$ (output). Looking at the graph:

• The highest point on the graph seems to be at $y = 3$.
• The lowest point on the graph appears to be $y = -3$.

Therefore, the range of the function is: $\boxed{[-3, 3]}$

2. Intervals of Increase:

A function is increasing where the graph rises as you move from left to right. In this case, the function increases in two intervals:

• From $x = -4$ to $x = -2$ (the graph moves upwards in this range).
• From $x = 0$ to $x = 2$.

Therefore, the intervals of increase are: $\boxed{(-4, -2)} \text{ and } \boxed{(0, 2)}$

3. Intervals of Decrease:

A function is decreasing where the graph falls as you move from left to right. The graph decreases in these intervals:

• From $x = -2$ to $x = 0$ (the graph moves downwards here).
• From $x = 2$ to $x = 4$.

Therefore, the intervals of decrease are: $\boxed{(-2, 0)} \text{ and } \boxed{(2, 4)}$

Would you like a more detailed explanation of how to determine increasing and decreasing intervals?

Here are five related questions you can explore:

1. How do you find the domain of a function from its graph?
2. What are local maxima and minima, and where are they in this graph?
3. Can you explain how to identify points of inflection from a graph?
4. How do derivatives relate to increasing and decreasing functions?
5. What is the importance of critical points in determining increasing or decreasing behavior?

Tip: When analyzing graphs, always check for key points like turning points (maxima and minima) to determine where the graph changes direction!