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

From the graph provided, I can see two distinct line segments on the coordinate plane. To determine the **domain** and **range**, we will focus on the x-coordinates for the domain and the y-coordinates for the range.

### Domain:
The **domain** represents the set of x-values covered by the graph.

- For the first line segment, the x-values range from approximately \( x = -2 \) to \( x = 1 \).
- For the second line segment, the x-values range from approximately \( x = 2 \) to \( x = 4 \).

Thus, the domain is the union of these two intervals.

**Set builder notation:**
\[
\{ x \mid -2 \leq x \leq 1 \} \cup \{ x \mid 2 \leq x \leq 4 \}
\]

**Interval notation:**
\[
[-2, 1] \cup [2, 4]
\]

### Range:
The **range** represents the set of y-values covered by the graph.

- For the first line segment, the y-values range from approximately \( y = 0 \) to \( y = 3 \).
- For the second line segment, the y-values range from approximately \( y = 1 \) to \( y = 2 \).

Thus, the range is the union of these two intervals.

**Set builder notation:**
\[
\{ y \mid 0 \leq y \leq 3 \} \cup \{ y \mid 1 \leq y \leq 2 \}
\]

**Interval notation:**
\[
[0, 3] \cup [1, 2]
\]

Would you like further details on how these intervals were determined or explanations on set notation?

### Follow-up questions:
1. What is the significance of domain and range in functions?
2. How can you determine if a graph represents a function using the vertical line test?
3. Can domain and range be infinite, and what does that look like on a graph?
4. How do you find domain and range for more complex functions (e.g., quadratic or rational functions)?
5. How do transformations (like shifting or scaling) affect the domain and range of a graph?

**Tip:** The domain of a function includes all x-values for which the function is defined, while the range includes all possible y-values the function can output.

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

Determine the domain and range of the graph, covering two line segments. The domain and range are expressed in both set builder notation and interval notation. This problem covers key mathematical concepts for students in Grades 7-10.

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