Let's analyze the graph to determine the domain and range of the function.

Domain:

The domain of a function is the set of all possible x-values (inputs) for which the function is defined.

• From the graph, the function starts at $x = -3$ (solid dot, indicating inclusion).
• It ends at $x = 2$ (open circle, indicating exclusion).

So, the domain is: $\text{Domain} = [-3, 2)$

Range:

The range of a function is the set of all possible y-values (outputs) the function can take.

• The highest point on the graph is at $y = 4$ (solid dot).
• The lowest point the function reaches is slightly below $y = -1$, at about $y = -1$ (open circle).

So, the range is: $\text{Range} = [-1, 4]$

Final Answer:

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

Would you like further clarification or details?

Here are 5 questions to explore further:

1. How do we determine when a dot on the graph means inclusion versus exclusion in the domain and range?
2. What is the difference between closed and open intervals?
3. How can the range change if the graph is stretched vertically or horizontally?
4. How do the domain and range change for different types of functions (e.g., polynomials, exponentials)?
5. Can there be cases where the domain is all real numbers? What would such a graph look like?

Tip: Always check for open and closed dots on the graph to know if endpoints are included in the domain or range.