https://file.aiquickdraw.com/mathbot/file/17300307063500849k3r4.jpg

To analyze this question, let's go through each part step-by-step.

### Step 1: Identify the Domain and Range
The graph shows four points: 
- \((-3, -1)\)
- \((0, -2)\)
- \((2, 0)\)
- \((3, 1)\)

1. **Domain**: The domain consists of all the x-values of the points in the graph. Therefore, the domain is:
   \[
   \{-3, 0, 2, 3\}
   \]

2. **Range**: The range consists of all the y-values of the points in the graph. Thus, the range is:
   \[
   \{-1, -2, 0, 1\}
   \]

### Step 2: Determine if the Relation is a Function
A relation is a function if each x-value is associated with only one y-value. In this graph, each x-value has a unique y-value associated with it:
- \(-3\) maps to \(-1\)
- \(0\) maps to \(-2\)
- \(2\) maps to \(0\)
- \(3\) maps to \(1\)

Since each x-value corresponds to only one y-value, this relation **is a function**.

### Step 3: Choose the Correct Answer
Now we match this information with the answer choices:

- **Option B** matches our findings:**
  - Domain: \(\{-3, 0, 2, 3\}\)
  - Range: \(\{-2, -1, 0, 1\}\)
  - It states that this is a function.

Thus, **Option B** is the correct answer.

---

Would you like a detailed breakdown of how functions and relations work? Here are some related questions:

1. How can you find the domain and range of other types of relations or functions?
2. What is the difference between a function and a non-function?
3. Can a function have more than one y-value for the same x-value?
4. How can you determine if a relation is a function just by looking at its graph?
5. What are real-world examples of functions and non-functions?

**Tip:** When identifying whether a relation is a function, use the "vertical line test" on the graph. If a vertical line intersects the graph at more than one point, the relation is not a function.

State the domain and range of the relation shown in the graph. Is the relation a function?

Understand how to determine the domain and range from a graph and verify if a relation is a function. This question uses the Vertical Line Test to analyze function properties and covers basic concepts in functions and relations, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation