# Blog

## What is a cubic function in math? ## What is the domain of the cube function?

• This is the Cube Function: It has origin symmetry. And it is an odd function. Its Domain is the Real Numbers: Its Range is also the Real Numbers:

## How many possible graphs are there for a cubic function?

• Up to an affine transformation, there are only three possible graphs for cubic functions. Cubic functions are fundamental for cubic interpolation . The roots, stationary points, inflection point and concavity of a cubic polynomial x3 − 3 x2 − 144 x + 432 (black line) and its first and second derivatives (red and blue).

## Why is the inflection point the origin of a cubic function?

• For a cubic function of the form the inflection point is thus the origin. As such a function is an odd function, its graph is symmetric with respect to the inflection point, and invariant under a rotation of a half turn around the inflection point. As these properties are invariant by similarity, the following is true for all cubic functions.  