An odd function has which property?

• A. f(-x) = f(x).
• B. f(-x) = -f(x).
• C. Graph is symmetric about the y-axis.
• D. Function is defined only for x>0.

Answer: (B)

An odd function is one where plugging in the negative input flips the sign of the output: f(-x) = -f(x) for all x in the domain. This property makes the graph symmetric with respect to the origin (rotate 180 degrees around the origin and it looks the same). The statement that f(-x) equals the negative of f(x) exactly captures this defining behavior, so it’s the best choice.

The other ideas describe different ideas. If f(-x) = f(x), that’s an even function with symmetry about the y-axis, not about the origin. Saying the graph is symmetric about the y-axis points to that evenness. And being defined only for x > 0 would prevent the function from exhibiting the necessary behavior across negative x, which odd functions require.