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State the domain and range for ach graph and then tellif the graph is a function (wite yes or no). in set builder notation

### 1. **Domain**:
The domain of the graph includes all the x-values where the graph exists. From the image, the graph starts at \( x = -4 \) and ends at \( x = 4 \), with open circles at these points, indicating that the endpoints are not included in the domain.

**Domain in set-builder notation**:
\[ \{ x \in \mathbb{R} \mid -4 < x < 4 \} \]

### 2. **Range**:
The range of the graph includes all the y-values that the graph reaches. The graph extends vertically from \( y = -5 \) to \( y = 5 \), with open circles at these points, meaning these values are not included in the range.

**Range in set-builder notation**:
\[ \{ y \in \mathbb{R} \mid -5 < y < 5 \} \]

### 3. **Is the Graph a Function?**:
To determine if the graph is a function, use the **Vertical Line Test**. Each vertical line drawn through any x-value in the domain intersects the graph at exactly one point, which means the graph passes the Vertical Line Test.

**Answer**: Yes, the graph is a function.

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Would you like more details or have any questions about this? Here are some related questions:

1. How do you interpret open and closed circles in the context of domain and range?
2. Can you describe the significance of the endpoints in determining whether a graph is a function?
3. What is the difference between continuous and discrete functions?
4. How does the shape of a piecewise linear function affect its domain and range?
5. Can you explain how to identify intervals of increase and decrease in a graph?

**Tip**: Open circles on a graph indicate that the specific point is not included in the function's domain or range, while closed circles indicate inclusion.

Understand the domain, range, and function status of a graph through clear explanations and set-builder notation examples. Learn how to apply the Vertical Line Test to determine if a graph is a function. Suitable for Grades 9-12.

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