https://file.aiquickdraw.com/mathbot/file/1725491579955nuov4hck.jpg

From the image provided, I see a graph with a vertical line test being applied to a function. The question asks for the **domain** and **range** of the function based on the graph.

### Domain:
The domain represents all the possible input values (x-values) for which the function is defined. In this graph, the curve appears to extend from about \(x = -4\) to \(x = 5\). Thus, the domain is approximately:
\[
\boxed{[-4, 5]}
\]

### Range:
The range represents all the possible output values (y-values) that the function can take. From the graph, it seems like the function's values range from \(y = -5\) to \(y = 3\). Thus, the range is approximately:
\[
\boxed{[-5, 3]}
\]

Would you like more details on how the domain and range are determined or any other clarification?

### Related Questions:
1. What is the difference between domain and range?
2. How would the domain or range change if the graph included open intervals or discontinuities?
3. How can you determine the domain and range of more complex functions (e.g., piecewise or trigonometric functions)?
4. What happens to the domain and range if the function has asymptotes?
5. How can transformations (like translations or stretches) affect the domain and range?

**Tip:** When determining domain and range from a graph, always check the x-axis for the domain and the y-axis for the range!

The image shows a graph, and the query is to determine the domain and range of the function based on the graph.

Learn how to determine the domain and range of a function by analyzing its graph. Understand the key concepts of functions, domain, range, and the vertical line test. Suitable for high school students.

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