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.
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