DOL: Domain and Range in Interval NotationQuestion1: What are the domain and range of the function?•A) Domain: [−3,2], Range: (−2,3]•B) Domain: (−3,2], Range: (−2,3]•C) Domain: [−3,2], Range: [−2,0]∪[3]•D) Domain: [−3,2], Range: (−∞,∞)

To solve this problem, we need to determine the correct domain and range for the function based on the given options.

### Domain:
The domain of a function consists of all possible input values (x-values) for which the function is defined.

### Range:
The range of a function consists of all possible output values (y-values) the function can produce.

Let's analyze the given options:

1. **Option A:**
   - **Domain:** \([-3, 2]\)
   - **Range:** \((-2, 3]\)

2. **Option B:**
   - **Domain:** \((-3, 2]\)
   - **Range:** \((-2, 3]\)

3. **Option C:**
   - **Domain:** \([-3, 2]\)
   - **Range:** \([-2, 0] \cup [3]\)

4. **Option D:**
   - **Domain:** \([-3, 2]\)
   - **Range:** \((-\infty, \infty)\)

### Conclusion:
- **Domain Comparison:**
  - Options A, C, and D suggest the domain includes \([-3, 2]\), while Option B suggests \((-3, 2]\), excluding \(-3\).
  
- **Range Comparison:**
  - Option A and B suggest similar ranges \((-2, 3]\).
  - Option C suggests the range is \([-2, 0] \cup [3]\), indicating the range is composed of two disjoint intervals.
  - Option D suggests the range includes all real numbers \((-\infty, \infty)\), which is a much larger set.

### Correct Answer:
To choose the correct answer, you need to determine which domain and range align with the characteristics of the given function. 

If the function is defined over a limited interval and has specific output values, **Option C: Domain: \([-3, 2]\), Range: \([-2, 0] \cup [3]\)** might be the correct answer since it suggests the function produces outputs in specific intervals and has gaps.

**Would you like a detailed explanation on how to determine the correct domain and range for specific types of functions?**

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Here are some related questions:
1. How do you find the domain of a function algebraically?
2. What is the difference between open and closed intervals in domain and range?
3. Can a function have more than one disjoint range interval?
4. What methods are used to graph a function and identify its domain and range?
5. How do vertical and horizontal asymptotes affect the range of a function?

**Tip:** Always check for any restrictions (like square roots or fractions) that could limit the domain when determining the domain of a function.

Explore how to determine the domain and range of a function in interval notation. This problem examines multiple-choice options for domain and range, providing a detailed analysis of each option's correctness. Suitable for high school students learning about functions and interval notation.

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