The graph you've uploaded shows a curve on a coordinate plane. Let's determine the domain and range based on the graph.

Domain:

The domain is the set of all possible $x$-values (horizontal axis) for which the function is defined.

• The curve starts from the far left and continues rightwards.
• On the left, it appears to extend indefinitely to the left (towards negative infinity), and it also includes $x = -2$ (the point where the curve changes direction).
• On the right, the curve ends at the point $x = 2$, and this point is an open circle, indicating that $x = 2$ is not included in the domain.

Thus, the domain is $(-\infty, 2)$.

Range:

The range is the set of all possible $y$-values (vertical axis) that the function can take.

• The curve starts from a maximum value at the top, which appears to occur at $y = 3$ and goes downward.
• The curve continues to extend downward towards $y = -\infty$.
• However, the curve only goes up to $y = 1$ at the right end, where $x = 2$ (but not including $y = 1$ since it is an open circle).

Thus, the range is $(-\infty, 3]$.

Summary:

• Domain: $(-\infty, 2)$
• Range: $(-\infty, 3]$

Would you like more details or have any questions?

Here are some related questions you might be interested in:

1. How do you find the domain and range of more complex functions?
2. What is the significance of open and closed circles in graphs?
3. Can a function have the same domain but different ranges?
4. How do transformations affect the domain and range of a function?
5. What are the differences between a function's graph and its inverse?

Tip: Always check the endpoints of the curve when determining domain and range; open circles indicate the value is not included, while closed circles indicate it is included.