Let's analyze the graph and answer the questions step by step:

1. Symmetry:

The graph does not appear to have symmetry with respect to the y-axis (not an even function) or the origin (not an odd function). Therefore, the function does not have symmetry.

2. Increasing/Decreasing:

• The function is increasing in the intervals: from $x = -\infty$ to point $A$, and again from point $O$ to point $C$.
• The function is decreasing in the intervals: from point $A$ to point $B$, and from point $B$ to point $O$.

3. Extrema:

• Relative Maximum: The function reaches a relative maximum at point $B$.
• Relative Minimum: The function has a relative minimum at point $O$.

4. End Behavior:

• As $x \to -\infty$, $y \to -\infty$ (the function tends downward).
• As $x \to +\infty$, $y \to +\infty$ (the function tends upward).

Summary of Answers:

• Symmetry: None
• Decreasing: From point $A$ to point $B$, and from point $B$ to point $O$.
• Increasing: From $x = -\infty$ to $A$, and from $O$ to $C$.
• Extrema: Maximum at $B$, Minimum at $O$.
• Relative Minimum: At $O$.
• Relative Maximum: At $B$.
• As $x \to -\infty$, $y \to -\infty$.
• As $x \to +\infty$, $y \to +\infty$.

Would you like more details or have any specific questions?

Here are five related questions to explore further:

1. How do you determine whether a function is even or odd by looking at the graph?
2. What is the significance of the relative maximum and minimum in real-world contexts?
3. Can a function have multiple relative maxima or minima?
4. How do you identify the intervals of increasing or decreasing behavior from a graph?
5. What is the difference between relative and absolute extrema?

Tip: Always check the behavior of a function at critical points (where the derivative is zero or undefined) to identify relative extrema.