Graph Using a Table of Values f(x) = cube root of x

$f (x) = \sqrt[3]{x}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{- 2}$

Step 2

Simplify $\sqrt[3]{- 2}$ .

Remove parentheses.

$y = \sqrt[3]{- 2}$

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

Rewrite $- 2$ as $- 1 (2)$ .

$y = \sqrt[3]{- 1 (2)}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = \sqrt[3]{{(- 1)}^{3} \cdot 2}$

Pull terms out from under the radical.

$y = - 1 \sqrt[3]{2}$

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

$y = - \sqrt[3]{2}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{- 1}$

Step 4

Simplify $\sqrt[3]{- 1}$ .

Remove parentheses.

$y = \sqrt[3]{- 1}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = \sqrt[3]{{(- 1)}^{3}}$

Pull terms out from under the radical, assuming real numbers.

$y = - 1$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{0}$

Step 6

Simplify $\sqrt[3]{0}$ .

Remove parentheses.

$y = \sqrt[3]{0}$

Rewrite $0$ as $0^{3}$ .

$y = \sqrt[3]{0^{3}}$

Pull terms out from under the radical, assuming real numbers.

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{1}$

Step 8

Simplify $\sqrt[3]{1}$ .

Remove parentheses.

$y = \sqrt[3]{1}$

Any root of $1$ is $1$ .

$y = 1$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{2}$

Step 10

Remove parentheses.

$y = \sqrt[3]{2}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \sqrt[3]{2} \\ - 1 & - 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & \sqrt[3]{2} \end{array}$

Step 12

Graph Using a Table of Values f(x) = cube root of x

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