To analyze the graph and solve the problem regarding the domain and range of $f(x)$, let’s break it down step by step:

(a) Domain of $f(x)$:

The domain represents all the possible values of $x$ for which $f(x)$ is defined. From the graph:

• There is a horizontal line segment from $x = -8$ to $x = -4$ at $y = -6$.
• The next segment appears to start at $x = -2$ and ends at $x = 5$, with breaks at $x = 1$ and $x = 3$.

Thus, the domain of $f(x)$ in interval notation is: [ \boxed{[-8, -4] \cup [-2, 1) \cup (1, 3) \cup [3, 5]} ]

(b) Range of $f(x)$:

The range consists of all the possible values of $y$ that $f(x)$ can take. From the graph:

• The first horizontal segment is at $y = -6$.
• The other points appear to range from $y = -6$ to $y = 9$.

Thus, the range of $f(x)$ in interval notation is: $\boxed{[-6, 9]}$

Would you like more details on any specific part of this analysis? Here are some related questions:

1. How do we handle discontinuities in domain or range?
2. Can you explain how to read specific points from the graph?
3. What does a break in the graph imply about the function's continuity?
4. How do you find the range of a piecewise graph with multiple segments?
5. What other forms of notation can be used to express domain and range?

Tip: Always check for open and closed points on a graph to identify whether values are included or excluded from the domain and range!