Algebra Examples

y = x^{3} - x

$y = x^{3} - x$

Step 1

Find the point at

x = - 2

$x = - 2$ .

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Step 1.1

Replace the variable

x

$x$ with

- 2

$- 2$ in the expression.

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

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

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

$- 2$ to the power of

3

$3$ .

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

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

Step 1.2.1.2

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

f (- 2) = - 8 + 2

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

f (- 2) = - 8 + 2

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

Step 1.2.2

Add

- 8

$- 8$ and

2

$2$ .

f (- 2) = - 6

$f (- 2) = - 6$

Step 1.2.3

The final answer is

- 6

$- 6$ .

- 6

$- 6$

- 6

$- 6$

Step 1.3

Convert

- 6

$- 6$ to decimal.

y = - 6

$y = - 6$

y = - 6

$y = - 6$

Step 2

Find the point at

x = - 1

$x = - 1$ .

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Step 2.1

Replace the variable

x

$x$ with

- 1

$- 1$ in the expression.

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

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

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

$- 1$ to the power of

3

$3$ .

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

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

Step 2.2.1.2

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

f (- 1) = - 1 + 1

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

f (- 1) = - 1 + 1

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

Step 2.2.2

Add

- 1

$- 1$ and

1

$1$ .

f (- 1) = 0

$f (- 1) = 0$

Step 2.2.3

The final answer is

0

$0$ .

0

$0$

0

$0$

Step 2.3

Convert

0

$0$ to decimal.

y = 0

$y = 0$

y = 0

$y = 0$

Step 3

Find the point at

x = 2

$x = 2$ .

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Step 3.1

Replace the variable

x

$x$ with

2

$2$ in the expression.

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

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

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

$2$ to the power of

3

$3$ .

f (2) = 8 - (2)

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

Step 3.2.1.2

Multiply

- 1

$- 1$ by

2

$2$ .

f (2) = 8 - 2

$f (2) = 8 - 2$

f (2) = 8 - 2

$f (2) = 8 - 2$

Step 3.2.2

Subtract

2

$2$ from

8

$8$ .

f (2) = 6

$f (2) = 6$

Step 3.2.3

The final answer is

6

$6$ .

6

$6$

6

$6$

Step 3.3

Convert

6

$6$ to decimal.

y = 6

$y = 6$

y = 6

$y = 6$

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}

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

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}

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

Step 6