Pre-Algebra Examples

$4 y^{3}$

Step 1

Find the point at $x = 0$ .

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Step 1.1

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

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

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify the numerator.

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Step 1.2.1.1

Multiply $2$ by $0$ .

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

Step 1.2.1.2

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

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

Step 1.2.1.3

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

$f (0) = \frac{0}{2}$

Step 1.2.2

Divide $0$ by $2$ .

$f (0) = 0$

Step 1.2.3

The final answer is $0$ .

$0$

Step 1.3

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = - 2$ .

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Step 2.1

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

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

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify the numerator.

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Step 2.2.1.1

Multiply $2$ by $- 2$ .

$f (- 2) = \frac{\sqrt[3]{- 4}}{2}$

Step 2.2.1.2

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

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Step 2.2.1.2.1

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

$f (- 2) = \frac{\sqrt[3]{- 1 \cdot 4}}{2}$

Step 2.2.1.2.2

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

$f (- 2) = \frac{\sqrt[3]{{(- 1)}^{3} \cdot 4}}{2}$

Step 2.2.1.3

Pull terms out from under the radical.

$f (- 2) = \frac{- 1 \sqrt[3]{4}}{2}$

Step 2.2.1.4

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

$f (- 2) = \frac{- \sqrt[3]{4}}{2}$

Step 2.2.2

Move the negative in front of the fraction.

$f (- 2) = - \frac{\sqrt[3]{4}}{2}$

Step 2.2.3

The final answer is $- \frac{\sqrt[3]{4}}{2}$ .

$- \frac{\sqrt[3]{4}}{2}$

Step 2.3

Convert $- \frac{\sqrt[3]{4}}{2}$ to decimal.

$y = - 0.79370052$

Step 3

Find the point at $x = - 1$ .

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Step 3.1

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

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

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify the numerator.

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Step 3.2.1.1

Multiply $2$ by $- 1$ .

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

Step 3.2.1.2

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

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Step 3.2.1.2.1

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

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

Step 3.2.1.2.2

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

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

Step 3.2.1.3

Pull terms out from under the radical.

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

Step 3.2.1.4

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

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

Step 3.2.2

Move the negative in front of the fraction.

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

Step 3.2.3

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

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

Step 3.3

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

$y = - 0.62996052$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

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

Step 4.2

Simplify the result.

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Step 4.2.1

Multiply $2$ by $1$ .

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

Step 4.2.2

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

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

Step 4.3

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

$y = 0.62996052$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

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

Step 5.2

Simplify the result.

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Step 5.2.1

Multiply $2$ by $2$ .

$f (2) = \frac{\sqrt[3]{4}}{2}$

Step 5.2.2

The final answer is $\frac{\sqrt[3]{4}}{2}$ .

$\frac{\sqrt[3]{4}}{2}$

Step 5.3

Convert $\frac{\sqrt[3]{4}}{2}$ to decimal.

$y = 0.79370052$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 0.794 \\ - 1 & - 0.63 \\ 0 & 0 \\ 1 & 0.63 \\ 2 & 0.794 \end{array}$

Step 7

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

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & - 0.794 \\ - 1 & - 0.63 \\ 0 & 0 \\ 1 & 0.63 \\ 2 & 0.794 \end{array}$

Step 8