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The graph provided shows the function \( f(x) \). We need to determine the domain and range of the function based on the visual information.

### 1. **Domain:**
The domain refers to all possible values of \( x \) for which the function is defined.

From the graph:
- The leftmost point is at \( x = -4 \), and it appears to be a closed point, meaning the function is defined at \( x = -4 \).
- The rightmost point is at \( x = 5 \), where there is a closed point as well.

However, there's a gap in the graph between \( x = 3 \) and \( x = 4 \), meaning the function is not defined in that interval.

Thus, the domain is the union of the intervals:
\[
\text{Domain} = [-4, 3] \cup [4, 5]
\]

### 2. **Range:**
The range refers to all possible values of \( y \) that the function can take.

From the graph:
- The lowest value of \( y \) is at \( y = -5 \), where the function starts.
- The highest point on the graph reaches \( y = 3 \).
- There are no gaps in the vertical direction between these two extreme values.

Thus, the range of the function is:
\[
\text{Range} = [-5, 3]
\]

### Summary:
- **Domain:** \( [-4, 3] \cup [4, 5] \)
- **Range:** \( [-5, 3] \)

Would you like further clarification or more details?

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Here are 5 related questions to expand your understanding:
1. How would the domain and range change if there were more gaps in the graph?
2. What happens to the domain if an open circle is used instead of a closed circle on the graph?
3. How can we find the domain and range of more complex functions, such as rational or trigonometric functions?
4. How does the vertical line test help us understand whether a graph represents a function?
5. Can a function have a range that is unbounded?

**Tip:** To confirm whether a graph represents a function, use the vertical line test—if a vertical line intersects the graph at more than one point, it's not a function.

The entire graph of the function f is shown in the figure. Write the domain and range of f as intervals or unions of intervals.

Learn how to determine the domain and range of a function by analyzing its graph. This problem covers core concepts of functions, graph interpretation, and identifying intervals of domain and range. Suitable for students in Grades 9-12.

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