Looking at the provided graph of the function $f(x)$, we need to determine the domain and range of the function.

Domain:

The domain refers to the set of all possible $x$-values for which the function is defined.

• The graph starts at $x = 0$ and ends at $x = 5$, but the graph at $x = 5$ has an open circle, indicating that the function is not defined at $x = 5$.
• Therefore, the domain is from $x = 0$ to $x = 5$, excluding $x = 5$.

Thus, the domain is: $[0, 5)$

Range:

The range refers to the set of all possible $y$-values the function can take.

• The maximum $y$-value on the graph is $y = 6$, where the graph starts.
• The graph reaches down to $y = 3$, which is the lowest point.
• It does not have any gaps in the $y$-values between 3 and 6, even though $x = 5$ is not included.

Thus, the range is: $[3, 6]$

Final Answer:

• Domain: $[0, 5)$
• Range: $[3, 6]$

Would you like further clarification or details on any part of this explanation? Here are some related questions that might help expand your understanding:

1. How do we handle open and closed circles when determining the domain or range?
2. What is the significance of the open circle at $x = 5$?
3. How would the domain or range change if the function extended beyond $x = 5$?
4. What are some common functions with similar domain or range constraints?
5. How does the range change if the graph shifts vertically?

Tip: When reading a graph, always check for open and closed points to identify if a value is included or excluded in the domain or range.