To solve for the domain and range of the function $h$ as shown in the graph:

(a) Domain:

• The domain represents all possible $x$-values for which the function $h(x)$ is defined.
• Observing the graph, the function starts at $x = -3$ and ends at $x = 4$.
• At $x = -3$, the point is filled, indicating that $x = -3$ is included.
• At $x = 4$, the point is open, meaning $x = 4$ is not included.

Thus, the domain in interval notation is: $[-3, 4)$

(b) Range:

• The range represents all possible $y$-values that the function $h(x)$ can take.
• The highest point on the graph occurs at $y = 4$, and the lowest point occurs at $y = -3$.
• The highest value $y = 4$ is included (filled point), while $y = -3$ is also included (open point on the right does not affect range).

Thus, the range in interval notation is: $[-3, 4]$

Final Answer:

• Domain: $[ -3, 4 )$
• Range: $[-3, 4]$

Would you like more details or have any questions about this?

Here are 5 related questions you might consider:

1. What is the difference between an open and closed interval?
2. How do you determine the domain from a graph of a function?
3. How do you determine the range of a function algebraically?
4. What is the significance of filled and open points on graphs in terms of domain and range?
5. How do you express a function's domain and range using set notation?

Tip: Always check for open or closed points at the boundaries of intervals when determining domain and range from a graph.