The graph provided represents a function $h$ that consists of two distinct pieces, each defined over specific intervals.

Domain:

To determine the domain, we need to identify all the $x$-values for which the function $h$ is defined. Looking at the graph:

• The left segment starts at $x = -5$ and ends at $x = -2$ (inclusive, because the points are filled).
• The right segment starts at $x = 1$ and ends at $x = 2$ (inclusive as well).

Thus, the domain of the function $h$ is the union of these intervals: [ \text{Domain} = [-5, -2] \cup [1, 2] ]

Range:

To find the range, we look at the corresponding $y$-values over the entire domain.

• For the left segment (from $x = -5$ to $x = -2$), the lowest $y$-value is approximately $-4$, and the highest $y$-value is 0.
• For the right segment (from $x = 1$ to $x = 2$), the lowest $y$-value is 2, and the highest is 5.

Thus, the range of the function $h$ is: [ \text{Range} = [-4, 0] \cup [2, 5] ]

Final Answer:

• Domain: $[-5, -2] \cup [1, 2]$
• Range: $[-4, 0] \cup [2, 5]$

Do you have any questions or need further details?

Here are five related questions:

1. What does it mean for a point on a graph to be "included" in the domain or range?
2. Can a function have a discontinuous domain or range, and why does this occur?
3. How do you interpret the endpoints of intervals on a graph?
4. Why are unions of intervals important when describing the domain or range of a function?
5. How can we tell if a function is continuous based on its graph?

Tip: When determining the domain and range from a graph, always check for open and closed circles at the endpoints, as these indicate whether the values are included or excluded.