To solve this problem, we need to analyze the domain and range of the graph shown in the image.

Domain:

The domain refers to all the possible $x$-values for which the graph is defined.

• The graph extends indefinitely to the left as the diagonal line continues, which means it covers all negative $x$-values.
• The rightmost point on the graph seems to occur at $x = 3$, and it appears to be a closed (filled) point.

Thus, the domain is: $(-\infty, 3]$

Range:

The range refers to all the possible $y$-values that the graph covers.

• The graph starts from the highest point at $y = 5$ (which is the highest point of the diagonal line as it extends indefinitely).
• The lowest $y$-value occurs at $y = 1$, which corresponds to a point at $x = 2$. This is the lowest part of the graph.

Thus, the range is: $(-\infty, 5]$

It seems like your initial answer for the domain is correct, but the range was reversed. The correct range should be $[1, 5]$, since the range should be listed in ascending order.

Would you like more details on the solution or have any other questions?

Here are 5 follow-up questions related to this topic:

1. How do we identify open and closed points on a graph for domain and range?
2. How does the slope of a line affect the domain and range of a function?
3. Can you explain how to determine whether a graph extends infinitely in a given direction?
4. What is the difference between domain and range in practical terms?
5. How does one apply domain and range in real-world problems?

Tip: Always list the range from the lowest $y$-value to the highest $y$-value, ensuring it reflects the vertical span of the graph.