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find the domain and range using set-builder notation

To express the domain and range using set-builder notation, let's analyze the function shown in the graph.

### Domain in Set-Builder Notation
The domain includes all \( x \) values from \(-2\) to \(3\), inclusive. In set-builder notation, the domain is written as:
\[
\{ x \mid -2 \leq x \leq 3 \}
\]
This reads as "the set of all \( x \) such that \( x \) is greater than or equal to \(-2\) and less than or equal to \(3\)."

### Range in Set-Builder Notation
The range includes all \( y \) values from \(-1\) to \(2\), inclusive. In set-builder notation, the range is written as:
\[
\{ y \mid -1 \leq y \leq 2 \}
\]
This reads as "the set of all \( y \) such that \( y \) is greater than or equal to \(-1\) and less than or equal to \(2\)."

### Final Answer:
- **Domain:** \( \{ x \mid -2 \leq x \leq 3 \} \)
- **Range:** \( \{ y \mid -1 \leq y \leq 2 \} \)

Would you like any additional details or explanations?

Here are five related questions:
1. How would the domain and range be expressed in interval notation?
2. What does set-builder notation look like for an absolute value function?
3. How do you express the domain and range of a function with a vertical asymptote?
4. What is the difference between set-builder notation and interval notation?
5. How can you describe the domain of a function with a discontinuity?

**Tip:** Set-builder notation is useful for specifying domains and ranges with conditions or restrictions, especially when the intervals are more complex.

Learn how to determine the domain and range of a function using set-builder notation. This detailed explanation covers the set-builder notation for both domain and range, with examples. Suitable for high school students.

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