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(Video) Graphing Cube Root Functions

by Kyle Ritter

Kyle Ritter has a good video explaining how to graph a cube root function.

(Video) Graph the Cube Root Function

by mathman1024

Here's a video by mathman1024 showing you how to graph the cubed root function. $$f(x)=\sqrt[3]{x}$$ If we draw a t-table of values we get $$\begin{array}{c|c} x&y\\ \hline -8&-2\\ -1&-1\\ 0&0\\ 1&1\\ 8&2 \end{array}$$

Now we can graph these points.

Connecting them gives us our cubed root graph!

Unlike the square root graph, the domain and range for the cubed root is all real numbers. $$D=(-\infty,\infty)\\ R=(-\infty,\infty)$$

Cube Root Graphs

In this lesson, we'll learn about cube root graphs and their important characteristics. We'll start with the parent function, $y=\sqrt[3]{x}$.

The cube root function is a continuous function, with no start or end point. Its domain is all real numbers.

Some major points for the parent function are:

$$\begin{align} (-8, -2) \\ (-1, -1) \\ (0,0) \\ (1,1) \\ (8,2) \\ \end{align}$$

If you plot these points, you will sketch out the cube root graph.

Transformations

Similar to other polynomial transformations we learned earlier, we can transform cube root functions!

Horizontal shift: shifting the function left or right by a value, $c$. Adding $c$ shifts the function to the left, and subtracting $c$ shifts the function to the right. $$y=\sqrt[3]{x +c }$$

Vertical shift: shifting the function up or down by a value, $d$. Adding $d$ shifts the function up, and subtracting $d$ shifts the function down. $$y=\sqrt[3]{x} +d$$

Dilation: stretching or shrinking the function by a value, $a$. If $a>1$, the function gets stretched, and if $0<a<1$, the function gets compressed. $$y=a\sqrt[3]{x}$$

Reflection: reflecting the function over either the $x$-axis or the $y$-axis. Negating the entire function reflects the function over the $x$-axis, and negative just the $x$ value reflects the function over the $y$-axis. $$y=-\sqrt[3]{x} \text{ OR } y=\sqrt[3]{-x}$$

Cube Root Graph

The next type of function we are going to tackle is the cube root function.

The cube root graph is one of our parent functions!

The graph of the cube root function is outlined in green.