02.24cbrt

# 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.

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