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To determine which of the given functions is odd, we need to apply the definition of an odd function. A function \( f(x) \) is odd if:

\[
f(-x) = -f(x) \quad \text{for all } x \text{ in the domain}.
\]

This implies that an odd function is symmetric about the origin.

Let's analyze each option:

- **A**: This function does not appear to be symmetric about the origin, so it is likely neither even nor odd.
- **B**: This function shows symmetry about the origin, indicating that it might be odd.
- **C**: This function does not exhibit origin symmetry, so it is not odd.
- **D**: This function appears symmetric about the \( y \)-axis, meaning it could be even, but not odd.

**Conclusion**: The correct answer is **B** since it shows symmetry about the origin, fulfilling the condition for an odd function.

Would you like more details or have any questions? Here are 5 related questions to expand the concept:

1. How can you algebraically test if a function is odd?
2. What is the difference between even and odd functions?
3. How does symmetry about the origin relate to odd functions?
4. Can a function be neither even nor odd? If so, provide an example.
5. How can you graphically determine if a function is even or odd?

**Tip**: When checking for odd functions graphically, look for symmetry around the origin—this is a key indicator!

Learn how to identify an odd function by analyzing its graph. Understand the symmetry about the origin and apply the condition f(-x) = -f(x). This question is suitable for high school students in Grades 9-12.

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