To determine the domain of the function shown in the graph, we need to identify all the $x$-values for which the function is defined. Here's how we analyze it:

Observations from the Graph:

1. The graph starts at $x = -8$, where it has a closed circle (indicating inclusion).
2. The function is continuous between $x = -8$ and $x = 16$.
3. At $x = 16$, there is an open circle (indicating exclusion).
4. From $x = 16$, the graph resumes at $x = 20$ (open circle) and continues to $x = 24$ (closed circle).

Domain in Notation:

• Set Notation: $\{x \,|\, -8 \leq x < 16 \text{ or } 20 < x \leq 24\}$

• Interval Notation: $[-8, 16) \cup (20, 24]$

This provides the domain of the function in both forms.

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Questions to Explore Further:

1. What is the difference between open and closed intervals in a domain?
2. How do you interpret gaps in the domain of a graph?
3. How can we identify the range of the function from the graph?
4. How does domain notation change for piecewise functions?
5. What are real-world examples of domains with restrictions?

Tip:

When writing domain in interval notation, always pay close attention to open (parentheses) and closed (brackets) endpoints on the graph.