To determine the domain of the given function, we need to identify the set of all possible $x$-values corresponding to the points on the graph.

From the image:

• There is a point at $x = -5$.
• There is a point at $x = -4$.
• There is a point at $x = 1$.
• There is a point at $x = 4$.
• There is a point at $x = 5$.

Thus, the domain consists of these $x$-values: $\{-5, -4, 1, 4, 5\}$.

The correct answer from the options is: {-5, -4, 1, 4, 5}.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the range of a function from a graph?
2. What is the difference between the domain and range of a function?
3. How can the domain of a function change if points are added or removed?
4. Can a function have an infinite domain?
5. What happens to the domain of a function if there are restrictions like square roots or division by zero?

Tip: Always look at the $x$-axis to determine the domain and the $y$-axis for the range when analyzing graphs.