Graph Using a Table of Values f(x) = cube root of x-2

$f (x) = \sqrt[3]{x} - 2$

Step 1

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

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

Step 2

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

Remove parentheses.

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

Simplify each term.

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

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

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

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

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

Pull terms out from under the radical.

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

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

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

Step 3

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

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

Step 4

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

Remove parentheses.

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

Simplify each term.

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

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

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

$y = - 1 - 2$

Subtract $2$ from $- 1$ .

$y = - 3$

Step 5

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

$y = \sqrt[3]{0} - 2$

Step 6

Simplify $\sqrt[3]{0} - 2$ .

Remove parentheses.

$y = \sqrt[3]{0} - 2$

Simplify each term.

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

$y = \sqrt[3]{0^{3}} - 2$

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

$y = 0 - 2$

Subtract $2$ from $0$ .

$y = - 2$

Step 7

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

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

Step 8

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

Remove parentheses.

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

Any root of $1$ is $1$ .

$y = 1 - 2$

Subtract $2$ from $1$ .

$y = - 1$

Step 9

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

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

Step 10

Remove parentheses.

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

Step 11

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

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

Step 12

Graph Using a Table of Values f(x) = cube root of x-2

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