Graph Using a Table of Values y = cube root of x-3

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

Step 1

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

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

Step 2

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

Subtract $3$ from $- 2$ .

$y = \sqrt[3]{- 5}$

Rewrite $- 5$ as ${(- 1)}^{3} \cdot 5$ .

Rewrite $- 5$ as $- 1 (5)$ .

$y = \sqrt[3]{- 1 (5)}$

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

$y = \sqrt[3]{{(- 1)}^{3} \cdot 5}$

Pull terms out from under the radical.

$y = - 1 \sqrt[3]{5}$

Rewrite $- 1 \sqrt[3]{5}$ as $- \sqrt[3]{5}$ .

$y = - \sqrt[3]{5}$

Step 3

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

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

Step 4

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

Subtract $3$ from $- 1$ .

$y = \sqrt[3]{- 4}$

Rewrite $- 4$ as ${(- 1)}^{3} \cdot 4$ .

Rewrite $- 4$ as $- 1 (4)$ .

$y = \sqrt[3]{- 1 (4)}$

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

$y = \sqrt[3]{{(- 1)}^{3} \cdot 4}$

Pull terms out from under the radical.

$y = - 1 \sqrt[3]{4}$

Rewrite $- 1 \sqrt[3]{4}$ as $- \sqrt[3]{4}$ .

$y = - \sqrt[3]{4}$

Step 5

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

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

Step 6

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

Subtract $3$ from $0$ .

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

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

Rewrite $- 3$ as $- 1 (3)$ .

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

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

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

Pull terms out from under the radical.

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

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

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

Step 7

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

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

Step 8

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

Subtract $3$ from $1$ .

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

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 9

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

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

Step 10

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

Subtract $3$ from $2$ .

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

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

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

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

$y = - 1$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \sqrt[3]{5} \\ - 1 & - \sqrt[3]{4} \\ 0 & - \sqrt[3]{3} \\ 1 & - \sqrt[3]{2} \\ 2 & - 1 \end{array}$

Step 12

Graph Using a Table of Values y = cube root of x-3

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