Let's break down the graph and answer the questions based on it.

a. The function is increasing on the interval(s):

The function increases when the slope is positive. From the graph, this occurs:

• From $x = -2$ to $x = 1$

So, the function is increasing on the interval $(-2, 1)$.

b. The function is decreasing on the interval(s):

The function decreases when the slope is negative. From the graph, this occurs:

• From $x = -4$ to $x = -2$
• From $x = 1$ to $x = 4$

So, the function is decreasing on the intervals $(-4, -2)$ and $(1, 4)$.

c. The function is constant on the interval(s):

The function is constant when the slope is zero (horizontal line). From the graph, this occurs:

• From $x = 4$ to $x = 10$

So, the function is constant on the interval $[4, 10)$.

d. The domain of the function:

The domain is the set of all possible $x$-values for which the function is defined. From the graph, the function is defined from $x = -5$ to $x = 10$.

So, the domain is $[-5, 10)$.

e. The range of the function:

The range is the set of all possible $y$-values that the function takes. From the graph, the function’s $y$-values range from $-6$ to $5$.

So, the range is $[-6, 5]$.

Would you like any further details or clarifications?

Here are five related questions you can explore:

1. What is the significance of a function being constant on an interval?
2. How can you determine the behavior of a function (increasing or decreasing) from its derivative?
3. How does the range of a function relate to its critical points?
4. What are the key differences between domain and range in a function?
5. How can piecewise functions be used to represent graphs like this?

Tip: When analyzing graphs, always check for open and closed intervals, especially if the graph continues indefinitely or ends abruptly!