https://file.aiquickdraw.com/mathbot/file/1726881482906wc09y9zo.jpg

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.

Write the domain and range of h as intervals or unions of intervals based on the provided graph.

Learn how to find the domain and range of a piecewise function by analyzing its graph. This problem involves interpreting intervals and unions of intervals based on a visual representation. Suitable for high school students in Grades 9-12.

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