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!