https://file.aiquickdraw.com/mathbot/file/1726851461744sa33w4d6.jpg

Let's analyze the provided graph and the questions.

1. **Does the graphed relation define a function?**

A relation is a function if, for each value of \( x \), there is only one corresponding value of \( y \). This is commonly checked using the *vertical line test*—if any vertical line intersects the graph more than once, it is not a function.

Looking at the graph, there are points where a vertical line intersects the curve more than once (for example, around \( x = 2 \) and \( x = 6 \)). Therefore, the graph **does not represent a function**.

2. **What is the domain of the graphed relation?**

The domain represents all possible values of \( x \) for which the relation is defined. From the graph, the curve stretches horizontally between \( x = -8 \) and \( x = 8 \). Hence, the domain is:

\[
\text{Domain}: [-8, 8]
\]

3. **What is the range of the graphed relation?**

The range represents all possible values of \( y \). The graph extends vertically between \( y = 2 \) and \( y = 8 \). Hence, the range is:

\[
\text{Range}: [2, 8]
\]

Would you like further details on any of these answers?

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Here are 5 related questions to expand your understanding:

1. What is the vertical line test, and how is it applied to determine a function?
2. How do we represent domains and ranges in interval notation?
3. Can a relation be a function if its graph has more than one vertical intersection at any \( x \)-value?
4. What is the difference between a relation and a function in mathematics?
5. Can a relation have more than one range for the same domain?

**Tip:** Always use the vertical line test to check if a graph represents a function—it quickly reveals if any \( x \)-value has more than one corresponding \( y \)-value.

Does the graphed relation define a function? What is the domain and range of the graphed relation?

Learn how to determine if a graphed relation is a function using the vertical line test. This problem covers understanding the domain and range from a graph, and explaining why the relation does not represent a function. Suitable for Grades 8-10.

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