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Solve the domain and range in interval notation using this graph

To determine the domain and range of the function represented by the graph, let's analyze the graph step by step.

### 1. **Domain**:
The domain represents all possible \(x\)-values that the function can take. In this case, we observe the graph starts at \(x = -4\) and ends at \(x = 4\), with the function defined at every point in between.

So, the domain in interval notation is:
\[
\text{Domain} = [-4, 4]
\]

### 2. **Range**:
The range represents all possible \(y\)-values that the function can take. From the graph:
- The lowest point on the graph occurs at \(y = -4\).
- The highest point on the graph occurs at \(y = 4\).

Thus, the range in interval notation is:
\[
\text{Range} = [-4, 4]
\]

If you have any further questions or would like a more detailed explanation, feel free to ask!

Here are 5 follow-up questions to expand your understanding:

1. How would the domain change if the graph extended beyond \(x = 4\)?
2. What happens to the range if the graph had a higher or lower maximum and minimum value?
3. How do you determine if a function is continuous from its graph?
4. Can the domain or range ever be represented by a union of intervals?
5. What would the domain and range be for a vertical or horizontal line?

**Tip**: Always check the graph for open or closed circles to determine whether endpoints are included in the domain and range.

Learn how to determine the domain and range of a function from its graph using interval notation. This detailed explanation covers key concepts in domain and range, suitable for high school students and anyone interested in graph analysis.

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