Pre-Algebra Examples

$8 y^{3} - 27$

Step 1

Find the point at $x = - 2$ .

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Step 1.1

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

$f (- 2) = \frac{\sqrt[3]{(- 2) + 27}}{2}$

Step 1.2

Simplify the result.

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Step 1.2.1

Add $- 2$ and $27$ .

$f (- 2) = \frac{\sqrt[3]{25}}{2}$

Step 1.2.2

The final answer is $\frac{\sqrt[3]{25}}{2}$ .

$\frac{\sqrt[3]{25}}{2}$

Step 1.3

Convert $\frac{\sqrt[3]{25}}{2}$ to decimal.

$y = 1.46200886$

Step 2

Find the point at $x = - 1$ .

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Step 2.1

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

$f (- 1) = \frac{\sqrt[3]{(- 1) + 27}}{2}$

Step 2.2

Simplify the result.

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Step 2.2.1

Add $- 1$ and $27$ .

$f (- 1) = \frac{\sqrt[3]{26}}{2}$

Step 2.2.2

The final answer is $\frac{\sqrt[3]{26}}{2}$ .

$\frac{\sqrt[3]{26}}{2}$

Step 2.3

Convert $\frac{\sqrt[3]{26}}{2}$ to decimal.

$y = 1.48124803$

Step 3

Find the point at $x = 0$ .

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Step 3.1

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

$f (0) = \frac{\sqrt[3]{(0) + 27}}{2}$

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

Add $0$ and $27$ .

$f (0) = \frac{\sqrt[3]{27}}{2}$

Step 3.2.1.2

Rewrite $27$ as $3^{3}$ .

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

Step 3.2.1.3

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

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

Step 3.2.2

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

$\frac{3}{2}$

Step 3.3

Convert $\frac{3}{2}$ to decimal.

$y = 1.5$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

$f (1) = \frac{\sqrt[3]{(1) + 27}}{2}$

Step 4.2

Simplify the result.

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Step 4.2.1

Add $1$ and $27$ .

$f (1) = \frac{\sqrt[3]{28}}{2}$

Step 4.2.2

The final answer is $\frac{\sqrt[3]{28}}{2}$ .

$\frac{\sqrt[3]{28}}{2}$

Step 4.3

Convert $\frac{\sqrt[3]{28}}{2}$ to decimal.

$y = 1.51829448$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

$f (2) = \frac{\sqrt[3]{(2) + 27}}{2}$

Step 5.2

Simplify the result.

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Step 5.2.1

Add $2$ and $27$ .

$f (2) = \frac{\sqrt[3]{29}}{2}$

Step 5.2.2

The final answer is $\frac{\sqrt[3]{29}}{2}$ .

$\frac{\sqrt[3]{29}}{2}$

Step 5.3

Convert $\frac{\sqrt[3]{29}}{2}$ to decimal.

$y = 1.53615841$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 1.462 \\ - 1 & 1.481 \\ 0 & 1.5 \\ 1 & 1.518 \\ 2 & 1.536 \end{array}$

Step 7

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

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & 1.462 \\ - 1 & 1.481 \\ 0 & 1.5 \\ 1 & 1.518 \\ 2 & 1.536 \end{array}$

Step 8