To find the domain and range of the function represented in the graph, we follow these steps:

Domain:

The domain of a function represents all possible input values (x-values) that the function can take.

From the graph, it appears the function starts at $x = -4$ (since there's a point on the graph at this x-value), and it ends at $x = 2$ (since the graph has a point here and does not extend further). Between these values, the function is continuous.

• Domain: $[-4, 2]$

Range:

The range of a function represents all possible output values (y-values) that the function can produce.

From the graph, we look at the lowest and highest points on the y-axis that the function reaches. The lowest point occurs around $y = -4$, and the highest point occurs around $y = 3$.

• Range: $[-4, 3]$

Summary:

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

Would you like further clarification or more details on this graph analysis?

Here are five related questions to consider:

1. What does it mean for a function to be continuous on its domain?
2. How can we determine whether the graph represents a function using the vertical line test?
3. What is the importance of identifying key points, such as intercepts, when analyzing a graph?
4. How can transformations (shifts, stretches) affect the domain and range of a function?
5. Can a function have a limited domain but an infinite range?

Tip: When analyzing graphs, always look for endpoints, turning points, and any discontinuities to accurately determine domain and range.