Cube Root Function and Graph

Power Functions

A power function has the form y = xn.

and for $n = \dfrac{1}{3}$, we get the cube root graph.

Cube Root Function and Graph

The standard cube root function is written as:

… …$y=x^\dfrac{1}{3} \qquad \text { or } y = \sqrt[3]{x}$


The cube root graph is the inverse of the standard cube graph (ie reflected across y = x)

Domain: $x \in R$

Range: $y \in R$

Intercepts at (0, 0)

There is no stationary point of inflection

but there is a point of inflection at (0, 0) where the graph turns from concave to convex.

  • At this point the derivative is undefined.
    • This means the graph is instantaneously vertical

All of the standard transformations can be applied to the cube root function.


Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License