Question

Which symmetry is represented by the function f(x) = x^3.

A. Reflectional symmetry in the y-axis
B. Rotational symmetry of 90°
C. Rotational symmetry of 180°
D. Reflectional symmetry in the x-axis

Answer 1

The function f(x) = x^3 represents an odd function with a rotational symmetry of 180° about the origin, meaning it has the same appearance when rotated 180 degrees.

Step-by-step explanation:

The function f(x) = x^3 is an example of an odd function. Odd functions have a specific type of symmetry; they are symmetric about the origin. This means that when reflecting the function about the y-axis and then about the x-axis, the function remains unchanged. Mathematically, a function f(x) is odd if f(x) = −f(−x). In this case, if we substitute −x into f(x), we get −(x^3) = −x^3, which is the negative of f(x), confirming that it is odd.

The correct symmetry for the given function f(x) = x^3 is C. Rotational symmetry of 180°. This is because rotating the graph of the function 180 degrees about the origin will align it with the original function, keeping the appearance unchanged.