https://file.aiquickdraw.com/mathbot/file/1728275192408o82no000.jpg

The question on your screen asks you to determine whether the graph represents a function and to identify its domain and range.

### 1. Does the relation define a function?
To check if a relation is a function, we apply the **Vertical Line Test**. A graph represents a function if and only if no vertical line intersects the graph at more than one point. 

From the image, the graph appears to be a horizontal curve (possibly a sideways parabola). Since a vertical line will intersect this curve at more than one point, this is **not a function**.

### 2. What is the domain of the relation?
The **domain** is the set of all possible \(x\)-values that the graph can take. Based on the graph, it spans horizontally from about \(x = -3\) to \(x = 3\). 
Thus, the domain is:
\[
\text{Domain: } [-3, 3]
\]

### 3. What is the range of the relation?
The **range** is the set of all possible \(y\)-values that the graph can take. From the graph, it spans vertically from about \(y = -2\) to \(y = 2\).
Thus, the range is:
\[
\text{Range: } [-2, 2]
\]

Would you like any further explanation or details on this problem?

### 5 Related Questions:
1. What is the significance of the Vertical Line Test in determining functions?
2. How do you find the domain and range for different types of graphs?
3. Can a curve represent both a function and a relation?
4. What are common types of relations that fail the Vertical Line Test?
5. How can you extend the idea of domain and range to 3-dimensional graphs?

**Tip:** Always remember, a relation is a function if every input \(x\) maps to exactly one output \(y\).

Does the graphed relation define a function, and what is the domain and range of the relation shown in the graph?

Learn how to identify whether a relation is a function using the Vertical Line Test. Also, determine the domain and range for a graphed relation. Suitable for high school students studying functions.

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