To determine if the relation in the graph defines a function, we apply the Vertical Line Test: if any vertical line drawn through the graph intersects it at more than one point, the relation is not a function. If no vertical line intersects the graph more than once, the relation is a function.

In this case, the graph depicts a curved line, and if you draw vertical lines, each one only intersects the curve at a single point. Therefore, the graphed relation does define a function.

Domain and Range:

• Domain: The graph extends from $x = -2$ (approximately) to positive infinity. Thus, the domain is $x \in [-2, \infty)$.
• Range: The lowest point on the graph appears to be at $y = 0$, and the curve extends upwards indefinitely. Therefore, the range is $y \in [0, \infty)$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the formal definition of a function in mathematics?
2. Can a relation that fails the vertical line test be considered a function if we restrict its domain?
3. How would you describe the difference between domain and range?
4. Can you give an example of a relation that is not a function?
5. What are other ways to determine the domain and range of a function?

Tip: When analyzing graphs, always start by identifying the key points such as intercepts, and then check the behavior as $x$ and $y$ approach infinity.