Based on the graph you provided, we can identify the domain and range of the function $f$ and write them in interval notation.

(a) Domain:

The domain refers to the set of all possible $x$-values (horizontal axis) for which the function is defined. From the graph:

• The function starts at $x = -3$ and extends to $x = 4$, where the open circle at $x = 4$ indicates that $x = 4$ is not included in the domain.

Thus, the domain in interval notation is: $\boxed{[-3, 4)}$

(b) Range:

The range refers to the set of all possible $y$-values (vertical axis) that the function takes. From the graph:

• The function starts at $y = 0$ and goes up to $y = 4$, where $y = 4$ is included because the point at $(1, 4)$ is filled in.

Thus, the range in interval notation is: $\boxed{[0, 4]}$

Let me know if you'd like further details or explanations! Here are some questions that expand on this topic:

1. What happens to the domain and range when a graph includes asymptotes?
2. How do you identify whether endpoints are included in interval notation?
3. Can a function's domain be infinite? How would it be expressed in interval notation?
4. How would the domain and range change if the graph had more discontinuities?
5. What are the implications of a vertical line test on determining the function's range?

Tip: Always pay attention to open and closed circles when determining domains and ranges. Closed circles mean the value is included, while open circles indicate exclusion.