https://file.aiquickdraw.com/mathbot/file/1729133912397p4crgb9f.jpg

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.

Determine whether the function has line symmetry and where the function is increasing and/or decreasing. Determine the extrema. Then identify the point as a relative maximum or relative minimum. Determine the end behavior.

Learn how to analyze a function's symmetry, determine increasing and decreasing intervals, identify relative extrema, and interpret end behavior from a graph. This detailed guide helps students in Grades 10-12 understand critical concepts in calculus using derivative tests.

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