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.