Algebra Examples

${(x^{2} + y^{2} - 1)}^{3} = x^{2}$ $y^{3}$

Step 1

Graph $y^{3}$ .

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Step 1.1

Find the point at $x = - 1$ .

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Step 1.1.1

Replace the variable $x$ with $- 1$ in the expression.

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

Step 1.1.2

Simplify the result.

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Step 1.1.2.1

Remove parentheses.

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

Step 1.1.2.2

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

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

Step 1.1.2.3

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

$f (- 1) = - 1$

Step 1.1.2.4

The final answer is $- 1$ .

$- 1$

Step 1.1.3

Convert $- 1$ to decimal.

$y = - 1$

Step 1.2

Find the point at $x = 0$ .

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Step 1.2.1

Replace the variable $x$ with $0$ in the expression.

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

Step 1.2.2

Simplify the result.

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Step 1.2.2.1

Remove parentheses.

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

Step 1.2.2.2

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

$f (0) = \sqrt[3]{0^{3}}$

Step 1.2.2.3

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

$f (0) = 0$

Step 1.2.2.4

The final answer is $0$ .

$0$

Step 1.2.3

Convert $0$ to decimal.

$y = 0$

Step 1.3

Find the point at $x = 1$ .

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Step 1.3.1

Replace the variable $x$ with $1$ in the expression.

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

Step 1.3.2

Simplify the result.

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Step 1.3.2.1

Remove parentheses.

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

Step 1.3.2.2

Any root of $1$ is $1$ .

$f (1) = 1$

Step 1.3.2.3

The final answer is $1$ .

$1$

Step 1.3.3

Convert $1$ to decimal.

$y = 1$

Step 1.4

Find the point at $x = - 2$ .

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Step 1.4.1

Replace the variable $x$ with $- 2$ in the expression.

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

Step 1.4.2

Simplify the result.

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Step 1.4.2.1

Remove parentheses.

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

Step 1.4.2.2

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

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Step 1.4.2.2.1

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

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

Step 1.4.2.2.2

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

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

Step 1.4.2.3

Pull terms out from under the radical.

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

Step 1.4.2.4

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

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

Step 1.4.2.5

The final answer is $- \sqrt[3]{2}$ .

$- \sqrt[3]{2}$

Step 1.4.3

Convert $- \sqrt[3]{2}$ to decimal.

$y = - 1.25992104$

Step 1.5

Find the point at $x = 2$ .

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Step 1.5.1

Replace the variable $x$ with $2$ in the expression.

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

Step 1.5.2

Simplify the result.

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Step 1.5.2.1

Remove parentheses.

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

Step 1.5.2.2

The final answer is $\sqrt[3]{2}$ .

$\sqrt[3]{2}$

Step 1.5.3

Convert $\sqrt[3]{2}$ to decimal.

$y = 1.25992104$

Step 1.6

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 2 & - 1.26 \\ - 1 & - 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 1.26 \end{array}$

Step 1.7

The cubic function can be graphed using the function behavior and the selected points.

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & - 1.26 \\ - 1 & - 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 1.26 \end{array}$

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & - 1.26 \\ - 1 & - 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 1.26 \end{array}$

Step 2

Plot each graph on the same coordinate system.

${(x^{2} + y^{2} - 1)}^{3} = x^{2}$

$y^{3}$

Step 3