Let's analyze the graph to determine the domain and range.

Domain:

The domain refers to the set of all possible x-values (input values) for the function. From the graph:

• The function includes points between $x = -5$ and $x = 6$, with both closed and open circles indicating certain values are included or excluded.

Analysis of Domain:

• There is a segment from $x = -5$ to $x = -2$, and both points seem to be closed circles, meaning these are included.
• Another segment appears between $x = 2$ and $x = 6$, where $x = 2$ has an open circle, indicating that this value is excluded, while $x = 6$ is included (closed circle).

Thus, the domain is: [ \text{Domain} = [-5, -2] \cup (2, 6] ]

Range:

The range refers to the set of all possible y-values (output values) for the function. From the graph:

• The y-values range from $y = -4$ to $y = 3$.

Analysis of Range:

• The function includes $y = -4$, but there is no point at $y = -3$ (open circle).
• There are points at $y = 0$, $y = 1$, and $y = 3$.

Thus, the range is: $\text{Range} = \{-4, 0, 1, 3\}$

Final Answer:

• Domain: $[-5, -2] \cup (2, 6]$
• Range: $\{-4, 0, 1, 3\}$

Would you like more details, or do you have any other questions?

Here are 5 related questions to expand on this:

1. How can you determine if a function is continuous from a graph?
2. What does an open circle on a graph indicate in terms of domain and range?
3. How does the vertical line test help in identifying functions on a graph?
4. Can the range of a function include both individual points and intervals?
5. What is the difference between a closed interval and an open interval?

Tip: Always observe both the x-axis and y-axis carefully, as the domain and range are about the horizontal and vertical extents of a function.