https://file.aiquickdraw.com/mathbot/file/1728275316937qorm51yf.jpg

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!

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 graphed relation defines a function using the Vertical Line Test. Includes step-by-step breakdown of domain and range for the graph. Suitable for high school students studying functions and graph analysis.

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