The problem asks whether the relation defined by the graph on the right is a function, and to determine its domain and range.

Step 1: Determine if it's a function

To check if the graphed relation is a function, apply the Vertical Line Test: If a vertical line intersects the graph at more than one point, the graph does not represent a function.

From the graph, a vertical line would intersect the curve at more than one point, particularly around values of $x = 3$ and $x = 7$. This means that for at least some $x$-values, there are multiple corresponding $y$-values. Therefore, the graph does not represent a function.

Step 2: Domain and Range

• Domain: The domain consists of all possible $x$-values for which the graph is defined. The graph spans $x$-values from $2$ to $8$, so the domain is: $\text{Domain}: [2, 8]$
• Range: The range consists of all possible $y$-values for which the graph is defined. The graph covers $y$-values from $1$ to $9$, so the range is: $\text{Range}: [1, 9]$

Final Answer:

• Does the graph define a function? No.
• Domain: [2, 8]
• Range: [1, 9]

Would you like a further breakdown or have any specific questions?

Here are 5 related questions for further practice:

1. How would the graph look if it defined a function?
2. What would the domain and range be if only part of the graph were considered?
3. Can a relation that fails the vertical line test ever be a function in another form?
4. What is the difference between the domain and range of a graph?
5. How can we use the vertical line test to analyze other types of curves?

Tip: Remember, the vertical line test is a quick and reliable way to determine if a graph represents a function!