https://file.aiquickdraw.com/mathbot/file/1726792378940s36cvphw.jpg

Let's analyze the graph and the problem presented in the image.

### 1. **Domain and Range:**
The domain and range represent the possible values of \( x \) and \( y \) that the graph covers.

- **Domain**: The domain refers to the set of all possible values of \( x \) in the relation.
  - From the graph, the line segment extends horizontally from \( x = -1 \) to \( x = 1 \). So, the domain is:
    \[
    -1 \leq x \leq 1
    \]

- **Range**: The range refers to the set of all possible values of \( y \).
  - From the graph, the line segment extends vertically from \( y = -1 \) to \( y = 1 \). Thus, the range is:
    \[
    -1 \leq y \leq 1
    \]

### 2. **Is it a function?**
To determine if the relation is a function, we use the **vertical line test**. If any vertical line crosses the graph at more than one point, the relation is not a function.

In this case, every vertical line intersects the graph at exactly one point. Therefore, **this relation is a function**.

### Final Answer:
- **Domain**: \( -1 \leq x \leq 1 \)
- **Range**: \( -1 \leq y \leq 1 \)
- **Is it a function?** Yes, it is a function.

Let me know if you'd like further details or have more questions!

Here are 5 follow-up questions for further exploration:
1. How does the vertical line test help determine if a relation is a function?
2. Can the domain and range be determined for more complex graphs, like parabolas or circles?
3. What would happen to the domain and range if the graph extended beyond the points \( (-1, 1) \) and \( (1, -1) \)?
4. What is the difference between a relation and a function?
5. Could you explain how to represent a function algebraically, graphically, and numerically?

**Tip**: Remember, a function must assign exactly one \( y \)-value for each \( x \)-value, which is why the vertical line test is so effective!

Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.

Learn how to analyze a graph to find the domain and range of a relation and determine whether the relation is a function using the vertical line test. This example involves a line segment extending from (-1, -1) to (1, 1) on the coordinate plane.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation