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Write the domain and range if the graph in set builder and interval notation 

Let's analyze each graph to determine the **domain** and **range**.

### Graph 19:
This graph represents a hyperbola, which has vertical and horizontal asymptotes.

- **Domain**: All \(x\)-values except the value where the vertical asymptote is located (i.e., \(x = 0\)).
  - **Set-builder notation**: \( \{ x \in \mathbb{R} \mid x \neq 0 \} \)
  - **Interval notation**: \( (-\infty, 0) \cup (0, \infty) \)

- **Range**: All \(y\)-values except the value where the horizontal asymptote is located (i.e., \(y = 0\)).
  - **Set-builder notation**: \( \{ y \in \mathbb{R} \mid y \neq 0 \} \)
  - **Interval notation**: \( (-\infty, 0) \cup (0, \infty) \)

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### Graph 20:
This graph appears to represent two points connected by a line segment.

- **Domain**: The \(x\)-values start at the \(x\)-coordinate of the leftmost point and end at the \(x\)-coordinate of the rightmost point.
  - **Set-builder notation**: \( \{ x \in \mathbb{R} \mid -3 \leq x \leq 2 \} \)
  - **Interval notation**: \( [-3, 2] \)

- **Range**: The \(y\)-values range from the bottommost point to the topmost point.
  - **Set-builder notation**: \( \{ y \in \mathbb{R} \mid -2 \leq y \leq 1 \} \)
  - **Interval notation**: \( [-2, 1] \)

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### Graph 21:
This graph consists of two rays extending from a common point, forming a "V" shape.

- **Domain**: The \(x\)-values include all real numbers since the rays extend indefinitely to the left and right.
  - **Set-builder notation**: \( \{ x \in \mathbb{R} \} \)
  - **Interval notation**: \( (-\infty, \infty) \)

- **Range**: The \(y\)-values begin from the lowest point (the vertex) and extend upward indefinitely.
  - **Set-builder notation**: \( \{ y \in \mathbb{R} \mid y \geq 0 \} \)
  - **Interval notation**: \( [0, \infty) \)

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Let me know if you'd like further clarifications or explanations. Here are 5 follow-up questions related to domain and range:

1. How would the domain and range change for a vertical parabola?
2. What happens to the domain if the graph has a vertical asymptote?
3. How can you identify the range when the graph has a horizontal asymptote?
4. What is the difference between open and closed intervals in interval notation?
5. How can you use set-builder notation to describe functions with restricted domains?

**Tip:** The domain and range are crucial when analyzing graphs because they tell us the possible values that \(x\) and \(y\) can take. Always check for any asymptotes or discontinuities!

Write the domain and range of the graph in set-builder and interval notation.

Learn how to write the domain and range for graphs using set-builder and interval notation. The problem covers key concepts in graphing functions, including asymptotes, domain, and range, with applications to hyperbolas, line segments, and rays. Suitable for Grades 8-10.

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