The graph shown in the image involves a piecewise function that consists of several sections. Let's break down how to find the domain and range of the function $h$.

1. Domain:

The domain refers to the set of all $x$-values for which the function is defined. Looking at the graph:

• The function starts at $x = -5$ and ends at $x = 5$.
• There are no breaks in the graph within this interval (aside from a possible open circle at a point, but this does not impact the overall domain).

Thus, the domain of the function is: $\boxed{[-5, 5]}$

2. Range:

The range is the set of all $y$-values that the function attains. Observing the graph:

• The lowest point on the graph occurs around $y = -3$.
• The highest point on the graph reaches $y = 3$.
• Based on the open and closed points, there are a few breaks in the range to note.

If there is an open circle at $(1, 3)$, then the value $y = 3$ is not included.

Thus, the range is likely: $\boxed{[-3, 3)}$ because the function reaches all values between $-3$ and slightly below 3, but not including 3 itself.

Would you like further clarification or a breakdown of any particular aspect? Here are 5 questions to help expand your understanding:

1. What is the significance of open and closed circles in determining the range?
2. How do we determine if a function has any breaks or discontinuities in its domain?
3. Could a domain ever be limited by restrictions on the function itself (e.g., division by zero)?
4. How would you represent a graph's domain if it included only discrete points?
5. What impact does the shape of a graph (e.g., increasing or decreasing) have on its range?

Tip: Always check for open or closed points on the graph when determining the range, as they indicate whether certain values are included or excluded.