Based on the given graph, let us determine the domain and range of the function:

Observing the Domain:

The domain is the set of all possible $x$-values for which the function is defined. From the graph:

• The function starts at $x = 1$ (closed dot, included) and ends at $x = 5$ (open dot, not included).

Thus, the domain is: $[1, 5)$

Observing the Range:

The range is the set of all possible $y$-values for which the function is defined. From the graph:

• The $y$-values start at $y = 1$ (closed dot, included) and go up to $y = 8$ (open dot, not included).

Thus, the range is: $[1, 8)$

Final Answer:

• Domain: $[1, 5)$
• Range: $[1, 8)$

Let me know if you would like a detailed explanation of these observations.

5 Related Questions:

1. What is the significance of open and closed dots in defining domain and range?
2. How would the domain or range change if the graph extended further?
3. What are other ways to represent domain and range (e.g., interval notation vs inequalities)?
4. How can you determine if a function is continuous from its graph?
5. What do the endpoints on a graph tell us about the behavior of a function?

Tip: Always pay attention to whether endpoints are open or closed—they play a crucial role in determining the exact domain and range.