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From the graph, we can break down the domain and range by analyzing the points and line segments in the plot. Let's go step by step:

### Domain:
The domain consists of all the x-values that the graph covers. The graph shows a combination of line segments and points, so we will look at the extent of the x-values.

1. **First Segment**: It appears between x = -6 and x = -4 (on the left side).
2. **Second Segment**: It starts at x = -1 and ends at x = 1.
3. **Third Segment**: Starts at x = 3 and ends at x = 8.

The domain is the union of all these intervals:
- \[ -6, -4 \] (for the first segment),
- \[ -1, 1 \] (for the second segment),
- \[ 3, 8 \] (for the third segment).

So, the **domain** is the set:
\[ D = [-6, -4] \cup [-1, 1] \cup [3, 8] \]

### Range:
The range consists of all the y-values the graph covers. We observe the vertical extent of the line segments.

1. **First Segment**: The y-value is constant at y = -4.
2. **Second Segment**: The y-values range from y = 1 to y = 5.
3. **Third Segment**: The y-values range from y = 1 to y = -2.
4. **Fourth Segment**: The y-values range from y = -2 to y = 3.

The range is the union of all these intervals:
- \[ -4 \] (for the first segment, a single value),
- \[ 1, 5 \] (for the second segment),
- \[ -2, 1 \] (for the third segment),
- \[ -2, 3 \] (for the fourth segment).

So, the **range** is the set:
\[ R = \{-4\} \cup [1, 5] \cup [-2, 1] \cup [-2, 3] \]

In simplified form, the range can be described as:
\[ R = [-4, 5] \]

### Final Answer:
- **Domain**: \[ D = [-6, -4] \cup [-1, 1] \cup [3, 8] \]
- **Range**: \[ R = [-4, 5] \]

Let me know if you need further clarification, or if you'd like more details about the process!

Here are some related questions to expand on this:
1. How do you determine the domain of a piecewise function graph?
2. What are the steps to find the range of a more complex graph?
3. Can you explain how vertical and horizontal line tests relate to domain and range?
4. How do discontinuities in a graph affect the domain and range?
5. What is the significance of closed vs open intervals in domain and range?

**Tip**: When reading graphs, it's essential to carefully observe where the lines or points exist and note any gaps or jumps, as these impact the domain and range.

Find the domain and range from the graph.

Learn how to find the domain and range of a graph containing multiple line segments and points. This problem involves breaking down the intervals for the x and y values, making it ideal for high school students in Grades 9-12.

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