https://file.aiquickdraw.com/mathbot/file/17282751829389ppwc8mi.jpg

The question in the image asks whether the graph defines a function and requests the domain and range. From the graph, we can see a straight line with a negative slope crossing the \(y\)-axis at \(y = 8\) and extending across the graph in a linear fashion.

### Does the graph represent a function?

Yes, the graph defines a function. To check this, we use the **Vertical Line Test**: if any vertical line drawn through the graph only intersects the graph at one point, then the graph represents a function. In this case, any vertical line intersects the graph at only one point, confirming that it is a function.

### Domain and Range:
- **Domain**: The graph extends infinitely in both directions along the \(x\)-axis, covering all real numbers. Therefore, the domain is:
  \[
  \text{Domain} = (-\infty, \infty)
  \]
  
- **Range**: Similarly, the graph covers all possible values along the \(y\)-axis, so the range is:
  \[
  \text{Range} = (-\infty, \infty)
  \]

Would you like more details or further clarification?

Here are some related questions:
1. What is the Vertical Line Test, and how does it work?
2. Can a graph represent a function if it is not a straight line?
3. How do you determine the domain of a function graphically?
4. What are the characteristics of a non-function in terms of a graph?
5. How does a line with a positive slope affect the function definition?

**Tip**: Always apply the vertical line test to determine if a relation is a function when working with graphs.

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

Learn how to determine if a graph represents a function using the Vertical Line Test, and understand how to find the domain and range of a linear graph. This problem is suitable for students in Grades 8-10 and covers key concepts of functions, domain, and range.

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