From the uploaded image, the graph shows a portion of a function with distinct endpoints.

Analyzing the Graph

1. Domain:
   The domain of a function is the set of all possible input values ($x$-values).
   From the graph, the function starts at $x = -2$ (closed circle) and ends at $x = 3$ (open circle).

   • Closed circle at $x = -2$: $x = -2$ is included.
   • Open circle at $x = 3$: $x = 3$ is not included.
     Hence, the domain is:
     $[-2, 3)$

2. Range:
   The range of a function is the set of all possible output values ($y$-values).
   From the graph, the lowest $y$-value is $-1$, corresponding to the point where $x = 3$ (open circle, so $y = -1$ is not included). The highest $y$-value is $4$, corresponding to the point where $x = -2$ (closed circle, so $y = 4$ is included).
   Hence, the range is:
   $(-1, 4]$

Final Answer

• Domain: $[-2, 3)$
• Range: $(-1, 4]$

Would you like a further explanation of how domain and range are determined?

Related Questions

1. What is the difference between open and closed intervals in a graph?
2. How would the domain and range change if the endpoints were flipped?
3. What is the domain and range of a vertical line on the graph?
4. Can a graph with breaks (discontinuities) still have a defined domain and range?
5. How do you express domain and range in set notation instead of interval notation?

Tip

When analyzing graphs, always pay attention to open and closed circles to ensure you determine whether values are included or excluded.