The image you provided shows a graph of a function with two marked points and a grid. You are asked to determine the domain and range of the function based on this graph.

Analyzing the Graph:

• The graph appears to be a part of a curve, most likely a quadratic function, starting at the leftmost red point and ending at the rightmost red point.
• The horizontal axis (x-axis) represents the domain of the function, and the vertical axis (y-axis) represents the range.

Domain:

• The domain is the set of all possible x-values for which the function is defined.
• From the graph, the x-values start from the x-coordinate of the leftmost point and end at the x-coordinate of the rightmost point.

Range:

• The range is the set of all possible y-values that the function can take.
• From the graph, the y-values start from the y-coordinate of the lowest point and go up to the y-coordinate of the highest point.

Determining the Values:

• Domain: It looks like the graph starts from $x = 0$ and ends at $x = 6$.
• Range: The lowest point on the graph seems to be at $y = -2$, and the highest point is at $y = 4$.

Conclusion:

• Domain: $[0, 6]$
• Range: $[-2, 4]$

Would you like a more detailed explanation or have any questions? Here are some related questions:

1. How do you find the domain and range of a function algebraically?
2. What types of functions have a domain and range that are not intervals?
3. How can you determine the domain and range of more complex functions?
4. What is the importance of the domain and range in real-world applications?
5. How does the shape of the graph affect the range of a function?

Tip: When analyzing a graph, always start by identifying the key points and their coordinates, as these often define the boundaries of the domain and range.