To find the domain of the function shown in the graph, we need to identify the range of $x$-values covered by the line segment from its starting point to its ending point.

Step-by-Step Solution:

1. Identify the Endpoints:

   • The line segment starts at the point $(-1, 1)$ and ends at $(3, 9)$.

2. Determine the Domain:

   • The domain is the set of all possible $x$-values between the endpoints.
   • From the graph, the $x$-values range from $-1$ to $3$.

3. Write the Domain in Set-Builder Notation:

   • In set-builder notation, the domain is represented as $\{ x | -1 \leq x \leq 3 \}$.

Answer:

The correct choice is:

• $\{ x | -1 \leq x \leq 3 \}$

Would you like more details on set-builder notation or have any other questions?

Here are some related questions to consider:

1. How do you determine the range of the function from a graph?
2. What is set-builder notation, and why is it useful?
3. How do domain and range differ in a function?
4. What are common errors when reading domains from graphs?
5. How does one identify continuous versus discrete domains?

Tip: When analyzing a graph for the domain, focus on the horizontal span of the graph (leftmost to rightmost points) to determine all possible $x$-values.