Algebra Examples

$y = x^{3} - x$

Step 1

Find the point at $x = - 2$ .

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Step 1.1

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

$f (- 2) = {(- 2)}^{3} - (- 2)$

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Raise $- 2$ to the power of $3$ .

$f (- 2) = - 8 - (- 2)$

Step 1.2.1.2

Multiply $- 1$ by $- 2$ .

$f (- 2) = - 8 + 2$

Step 1.2.2

Add $- 8$ and $2$ .

$f (- 2) = - 6$

Step 1.2.3

The final answer is $- 6$ .

$- 6$

Step 1.3

Convert $- 6$ to decimal.

$y = - 6$

Step 2

Find the point at $x = - 1$ .

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Step 2.1

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

$f (- 1) = {(- 1)}^{3} - (- 1)$

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Raise $- 1$ to the power of $3$ .

$f (- 1) = - 1 - (- 1)$

Step 2.2.1.2

Multiply $- 1$ by $- 1$ .

$f (- 1) = - 1 + 1$

Step 2.2.2

Add $- 1$ and $1$ .

$f (- 1) = 0$

Step 2.2.3

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

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Step 3.1

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

$f (2) = {(2)}^{3} - (2)$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Raise $2$ to the power of $3$ .

$f (2) = 8 - (2)$

Step 3.2.1.2

Multiply $- 1$ by $2$ .

$f (2) = 8 - 2$

Step 3.2.2

Subtract $2$ from $8$ .

$f (2) = 6$

Step 3.2.3

The final answer is $6$ .

$6$

Step 3.3

Convert $6$ to decimal.

$y = 6$

Step 4

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

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & 0 \\ 0 & 0 \\ 1 & 0 \\ 2 & 6 \end{array}$

Step 5

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & 0 \\ 0 & 0 \\ 1 & 0 \\ 2 & 6 \end{array}$

Step 6