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 $y$.