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To analyze the graph of the function \( h \), we need to determine both the **domain** and **range** based on the behavior of the graph.

### Domain:
The domain consists of all possible values of \( x \) for which the function is defined. From the graph:
- The function starts at \( x = -4 \) and continues up to \( x = 5 \), with a break between \( x = -1 \) and \( x = 2 \), where the function is not defined.
- The points at \( x = -4 \) and \( x = 5 \) are open circles, indicating that these values are not included in the domain.

Thus, the domain is the union of the intervals:
\[
(-4, -1] \cup [2, 5)
\]

### Range:
The range consists of all possible values of \( y \) that the function takes.
- The lowest point is at \( y = -1 \) (at \( x = -2 \)).
- The highest point is at \( y = 4 \) (at \( x = -4 \)).
- The function does not cover values between \( y = 0 \) and \( y = 1 \) based on the break in the graph.

Thus, the range is:
\[
[-1, 0] \cup [2, 4]
\]

### Final Answer:
- **Domain:** \( (-4, -1] \cup [2, 5) \)
- **Range:** \( [-1, 0] \cup [2, 4] \)

Would you like further details or have any questions?

Here are 5 related questions:
1. How does one determine the domain and range from a graph?
2. What is the significance of open and closed circles on a graph?
3. How do breaks in the graph affect the domain and range?
4. Can a function have more than one disconnected interval in its domain?
5. What is the difference between the domain of a function and its range?

**Tip:** Open circles on a graph mean that the point is not included in the domain or range, while closed circles mean the point is included.

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

Analyze the domain and range of the function h based on its graph. Identify key intervals and breaks in the graph to determine the valid x-values (domain) and y-values (range). Suitable for students in Grades 9-12.

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