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?

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.