To determine the correct answers, let’s analyze the graph step by step, based on each option provided:

1. Domain:

   • The domain represents the set of all $x$-values for which the graph has points.
   • Observing the graph, the $x$-values range from $x = -3$ (open circle, so not included) to $x = 4$ (closed circle, so included).
   • Therefore, the domain is $(-3, 4]$, which matches Option A.

2. Range:

   • The range represents the set of all $y$-values for which the graph has points.
   • Observing the graph, the $y$-values range from $y = -3$ (open circle, so not included) to $y = 3$.
   • Therefore, the range is $(-3, 3]$, which matches Option B.

3. Increasing:

   • The graph is increasing on intervals where it goes upward as $x$ increases.
   • Here, the graph increases from $x = -3$ to $x = -1$.
   • This matches Option C: increasing $(-3, -1)$.

4. Decreasing:

   • The graph is decreasing on intervals where it goes downward as $x$ increases.
   • The graph decreases from $x = -1$ to $x = 4$.
   • This matches Option D: decreasing $(-1, 4)$.

5. Positive:

   • The function is positive when it lies above the $x$-axis ($y > 0$).
   • Observing the graph, it is above the $x$-axis between $x = -2$ and $x = 2$.
   • This matches Option E: positive $(-2, 2)$.

6. Negative:

   • The function is negative when it lies below the $x$-axis ($y < 0$).
   • Observing the graph, it is below the $x$-axis in the intervals $(-3, -2)$ and $(2, 4]$.
   • This matches Option F: negative $(-3, -2), (2, 4]$.

Final Answer:

The correct selections are:

• A. domain: (-3, 4]
• B. range: (-3, 3]
• C. increasing: (-3, -1)
• D. decreasing: (-1, 4)
• E. positive: (-2, 2)
• F. negative: (-3, -2), (2, 4]

Would you like further clarification on any of these points, or do you need more details on a specific part of the analysis?

Relative Questions:

1. What is the importance of identifying the domain and range in a function's graph?
2. How can one determine intervals of increase and decrease in a function graphically?
3. Why are open and closed circles used in graphs, and what do they signify?
4. What are some real-world applications of interpreting function positivity and negativity?
5. How do you determine if a function is positive or negative in a given interval?

Tip: Always pay close attention to open and closed circles on graphs as they indicate whether endpoints are included in the domain and range.