Algebra Examples

$y^{3} = 8 x$

Step 1

Find the point at $x = - 1$ .

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Step 1.1

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

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

Step 1.2

Simplify the result.

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Step 1.2.1

Remove parentheses.

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

Step 1.2.2

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

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

Step 1.2.3

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

$f (- 1) = 2 \cdot - 1$

Step 1.2.4

Multiply $2$ by $- 1$ .

$f (- 1) = - 2$

Step 1.2.5

The final answer is $- 2$ .

$- 2$

Step 1.3

Convert $- 2$ to decimal.

$y = - 2$

Step 2

Find the point at $x = 0$ .

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Step 2.1

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

$f (0) = 2 \sqrt[3]{0}$

Step 2.2

Simplify the result.

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Step 2.2.1

Remove parentheses.

$f (0) = 2 \sqrt[3]{0}$

Step 2.2.2

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

$f (0) = 2 \sqrt[3]{0^{3}}$

Step 2.2.3

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

$f (0) = 2 \cdot 0$

Step 2.2.4

Multiply $2$ by $0$ .

$f (0) = 0$

Step 2.2.5

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 1$ .

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Step 3.1

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

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

Step 3.2

Simplify the result.

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Step 3.2.1

Remove parentheses.

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

Step 3.2.2

Any root of $1$ is $1$ .

$f (1) = 2 \cdot 1$

Step 3.2.3

Multiply $2$ by $1$ .

$f (1) = 2$

Step 3.2.4

The final answer is $2$ .

$2$

Step 3.3

Convert $2$ to decimal.

$y = 2$

Step 4

Find the point at $x = - 2$ .

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Step 4.1

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

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

Step 4.2

Simplify the result.

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Step 4.2.1

Remove parentheses.

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

Step 4.2.2

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

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Step 4.2.2.1

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

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

Step 4.2.2.2

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

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

Step 4.2.3

Pull terms out from under the radical.

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

Step 4.2.4

Simplify the expression.

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Step 4.2.4.1

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

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

Step 4.2.4.2

Multiply $- 1$ by $2$ .

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

Step 4.2.5

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

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

Step 4.3

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

$y = - 2.51984209$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

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

Step 5.2

Simplify the result.

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Step 5.2.1

Remove parentheses.

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

Step 5.2.2

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

$2 \sqrt[3]{2}$

Step 5.3

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

$y = 2.51984209$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 2.52 \\ - 1 & - 2 \\ 0 & 0 \\ 1 & 2 \\ 2 & 2.52 \end{array}$

Step 7

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

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & - 2.52 \\ - 1 & - 2 \\ 0 & 0 \\ 1 & 2 \\ 2 & 2.52 \end{array}$

Step 8