02.24cbrt

# Cube Root Function and Graph

## Power Functions

A power function has the form y = x^{n}.

- For n = 1, we get a linear graph,
- For n = 2 we get a parabola,
- For n = 3 we get a cubic.
- For n = –1, we get a hyperbola.
- For n = –2, we get a truncus

- For $n = \dfrac{1}{2}$, we get the square root graph.

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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