The graph shown represents a function $f$, and we are tasked with determining its domain and range in interval notation.

Domain:

The domain of a function refers to all possible $x$-values for which the function is defined. From the graph:

• The $x$-values start at $x = -3$ (where the function has a closed point, indicating inclusion).
• The $x$-values extend to $x = 4$ (where the function has an open point, indicating exclusion).

Thus, the domain of the function $f$ is: $[-3, 4)$

Range:

The range of a function refers to all possible $y$-values that the function can take. From the graph:

• The $y$-values start at $y = -5$ (open point, so this value is excluded).
• The $y$-values extend to $y = 4$ (closed point, so this value is included).

Thus, the range of the function $f$ is: $(-5, 4]$

Summary:

• Domain: $[-3, 4)$
• Range: $(-5, 4]$

Would you like more details on interval notation, or have any specific questions?

Here are some related questions you might find helpful:

1. What does a closed point on a graph signify?
2. How can we determine if a point is included in the domain or range?
3. What is the difference between open and closed intervals in interval notation?
4. Can a function have multiple disconnected intervals in its domain or range?
5. How do we determine the behavior of a function at endpoints?

Tip: Closed intervals (with square brackets) mean the endpoint is included, while open intervals (with parentheses) mean the endpoint is not included.