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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.

The entire graph of f is given. State the domain and range of f. The domain D of the function f is.

This problem involves analyzing a graph of a function to determine its domain and range. The function spans the x-values from 0 to 5, excluding 5, and y-values from 3 to 6. This problem is suitable for students in Grades 7-9.

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