What type of symmetry does the function f(x) = x³ have?

The function f(x) = x³ exhibits rotational symmetry, which means that its graph remains unchanged when rotated about the origin by 180 degrees. This characteristic arises due to the function being an odd function, where the property f(-x) = -f(x) holds true.

In practical terms, if you were to rotate the graph of f(x) = x³ around the origin, the shape would look the same after a 180-degree rotation, indicating this type of symmetry. The curve passes through the origin and is symmetric with respect to the origin, reinforcing the concept of rotational symmetry.

While vertical and horizontal symmetries pertain to reflections across the y-axis and x-axis respectively, and reflectional symmetry relates to mirroring aspects of a graph across a line, none of these concepts apply to this function in the same way. Thus, the proper classification of the symmetry for f(x) = x³ is rotational symmetry.