Which statement describes a property of an odd function?

Which statement describes a property of an odd function?

• A. Symmetric across the y-axis
• B. Symmetric about the origin
• C. Only odd exponents
• D. Cannot shift up, down, left or right

Answer: (B)

Odd functions have symmetry about the origin: the graph looks the same when rotated 180 degrees around the origin, which means f(-x) = -f(x). This means if a point (x, y) is on the graph, then (-x, -y) is also on the graph. That description—being symmetric about the origin—captures the defining property of odd functions. Reflecting across the y-axis describes even functions, where f(-x) = f(x). Having only odd exponents can describe certain odd polynomials, but it’s not the universal property of all odd functions. And the idea that you cannot shift the graph up, down, left, or right isn’t correct, because shifting typically destroys the origin symmetry, so it isn’t a property that all odd functions share.

Odd functions have symmetry about the origin: the graph looks the same when rotated 180 degrees around the origin, which means f(-x) = -f(x). This means if a point (x, y) is on the graph, then (-x, -y) is also on the graph. That description—being symmetric about the origin—captures the defining property of odd functions.

Reflecting across the y-axis describes even functions, where f(-x) = f(x). Having only odd exponents can describe certain odd polynomials, but it’s not the universal property of all odd functions. And the idea that you cannot shift the graph up, down, left, or right isn’t correct, because shifting typically destroys the origin symmetry, so it isn’t a property that all odd functions share.