https://file.aiquickdraw.com/mathbot/file/1726612722209c2t8soz2.jpg

To determine if the relation in the graph defines a function, we apply the **Vertical Line Test**: if any vertical line drawn through the graph intersects it at more than one point, the relation is not a function. If no vertical line intersects the graph more than once, the relation is a function.

In this case, the graph depicts a curved line, and if you draw vertical lines, each one only intersects the curve at a single point. Therefore, the graphed relation **does define a function**.

### Domain and Range:
- **Domain**: The graph extends from \(x = -2\) (approximately) to positive infinity. Thus, the domain is \(x \in [-2, \infty)\).
- **Range**: The lowest point on the graph appears to be at \(y = 0\), and the curve extends upwards indefinitely. Therefore, the range is \(y \in [0, \infty)\).

Would you like further details or have any questions? 

Here are 5 related questions:
1. What is the formal definition of a function in mathematics?
2. Can a relation that fails the vertical line test be considered a function if we restrict its domain?
3. How would you describe the difference between domain and range?
4. Can you give an example of a relation that is not a function?
5. What are other ways to determine the domain and range of a function?

**Tip**: When analyzing graphs, always start by identifying the key points such as intercepts, and then check the behavior as \(x\) and \(y\) approach infinity.

Decide whether the relation defined by the graph defines a function, and give the domain and range.

Learn how to determine if a graphed relation defines a function using the Vertical Line Test. The problem includes finding the domain and range of the function. This lesson is suitable for students in Grades 9-12.

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