To determine the domain and range of the graph, let's analyze the visible points and the curve in the image.

Domain

The domain is the set of all possible $x$-values. Based on the graph, it appears that the graph spans horizontally from approximately $x = -5$ to $x = 5$ along the $x$-axis. This indicates that the domain is: $[-5, 5]$

Range

The range is the set of all possible $y$-values. Looking at the graph, it seems to extend vertically from $y = -10$ up to $y = 5$. Thus, the range is: $[-10, 5]$

In summary:

• Domain: $[-5, 5]$
• Range: $[-10, 5]$

Would you like a further breakdown or have any specific questions?

Related Questions to Explore:

1. How would the domain change if the graph extended further left or right?
2. What would the range be if the highest point was at $y = 10$ instead?
3. How do closed vs. open points on a graph affect the domain and range?
4. Can a function have multiple domains or ranges, and under what conditions?
5. How do transformations (e.g., shifts, stretches) impact the domain and range?

Tip:

When determining the domain and range from a graph, focus on the horizontal extent for domain and the vertical extent for range.