To find the domain and range of the function shown in the graph, we will look at the horizontal and vertical extents of the graph, respectively.

Domain:

The domain refers to the set of all possible input values (x-values) for which the function is defined.

• The graph starts at $x = 1$ (a closed dot, meaning the function is defined at this point).
• The graph ends at $x = 6$ (an open dot, meaning the function is not defined at this point).

Therefore, the domain is $[1, 6)$ in interval notation.

Range:

The range refers to the set of all possible output values (y-values) that the function can take.

• The lowest point on the graph is $y = -8$, where the graph ends (open dot).
• The highest point on the graph is $y = 2$, which is reached at the peak.

Therefore, the range is $(-8, 2]$ in interval notation.

Final Answer:

• Domain: $[1, 6)$
• Range: $(-8, 2]$

Would you like further details or explanations?

Here are 5 questions to expand your understanding:

1. What happens if the open or closed dots change on the graph?
2. How would you describe the difference between domain and range?
3. Can you determine the function's continuity based on this graph?
4. How do open and closed intervals affect domain and range?
5. What type of function could represent this graph (e.g., quadratic, cubic)?

Tip: Always check the nature of the dots (open or closed) to determine whether to include or exclude boundary points in the domain and range.