Algebra Examples

y = x^{3} - 4 x

$y = x^{3} - 4 x$

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} - 4 \cdot - 2

$f (- 2) = {(- 2)}^{3} - 4 \cdot - 2$

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 - 4 \cdot - 2

$f (- 2) = - 8 - 4 \cdot - 2$

Step 1.2.1.2

Multiply

- 4

$- 4$ by

- 2

$- 2$ .

f (- 2) = - 8 + 8

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

f (- 2) = - 8 + 8

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

Step 1.2.2

Add

- 8

$- 8$ and

8

$8$ .

f (- 2) = 0

$f (- 2) = 0$

Step 1.2.3

The final answer is

0

$0$ .

0

$0$

0

$0$

Step 1.3

Convert

0

$0$ to decimal.

y = 0

$y = 0$

y = 0

$y = 0$

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} - 4 \cdot - 1

$f (- 1) = {(- 1)}^{3} - 4 \cdot - 1$

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 - 4 \cdot - 1

$f (- 1) = - 1 - 4 \cdot - 1$

Step 2.2.1.2

Multiply

- 4

$- 4$ by

- 1

$- 1$ .

f (- 1) = - 1 + 4

$f (- 1) = - 1 + 4$

f (- 1) = - 1 + 4

$f (- 1) = - 1 + 4$

Step 2.2.2

Add

- 1

$- 1$ and

4

$4$ .

f (- 1) = 3

$f (- 1) = 3$

Step 2.2.3

The final answer is

3

$3$ .

3

$3$

3

$3$

Step 2.3

Convert

3

$3$ to decimal.

y = 3

$y = 3$

y = 3

$y = 3$

Step 3

Find the point at

x = 0

$x = 0$ .

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Step 3.1

Replace the variable

x

$x$ with

0

$0$ in the expression.

f (0) = {(0)}^{3} - 4 \cdot 0

$f (0) = {(0)}^{3} - 4 \cdot 0$

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

Raising

0

$0$ to any positive power yields

0

$0$ .

f (0) = 0 - 4 \cdot 0

$f (0) = 0 - 4 \cdot 0$

Step 3.2.1.2

Multiply

- 4

$- 4$ by

0

$0$ .

f (0) = 0 + 0

$f (0) = 0 + 0$

f (0) = 0 + 0

$f (0) = 0 + 0$

Step 3.2.2

Add

0

$0$ and

0

$0$ .

f (0) = 0

$f (0) = 0$

Step 3.2.3

The final answer is

0

$0$ .

0

$0$

0

$0$

Step 3.3

Convert

0

$0$ to decimal.

y = 0

$y = 0$

y = 0

$y = 0$

Step 4

Find the point at

x = 1

$x = 1$ .

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Step 4.1

Replace the variable

x

$x$ with

1

$1$ in the expression.

f (1) = {(1)}^{3} - 4 \cdot 1

$f (1) = {(1)}^{3} - 4 \cdot 1$

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

One to any power is one.

f (1) = 1 - 4 \cdot 1

$f (1) = 1 - 4 \cdot 1$

Step 4.2.1.2

Multiply

- 4

$- 4$ by

1

$1$ .

f (1) = 1 - 4

$f (1) = 1 - 4$

f (1) = 1 - 4

$f (1) = 1 - 4$

Step 4.2.2

Subtract

4

$4$ from

1

$1$ .

f (1) = - 3

$f (1) = - 3$

Step 4.2.3

The final answer is

- 3

$- 3$ .

- 3

$- 3$

- 3

$- 3$

Step 4.3

Convert

- 3

$- 3$ to decimal.

y = - 3

$y = - 3$

y = - 3

$y = - 3$

Step 5

Find the point at

x = 2

$x = 2$ .

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Step 5.1

Replace the variable

x

$x$ with

2

$2$ in the expression.

f (2) = {(2)}^{3} - 4 \cdot 2

$f (2) = {(2)}^{3} - 4 \cdot 2$

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Raise

2

$2$ to the power of

3

$3$ .

f (2) = 8 - 4 \cdot 2

$f (2) = 8 - 4 \cdot 2$

Step 5.2.1.2

Multiply

- 4

$- 4$ by

2

$2$ .

f (2) = 8 - 8

$f (2) = 8 - 8$

f (2) = 8 - 8

$f (2) = 8 - 8$

Step 5.2.2

Subtract

8

$8$ from

8

$8$ .

f (2) = 0

$f (2) = 0$

Step 5.2.3

The final answer is

0

$0$ .

0

$0$

0

$0$

Step 5.3

Convert

0

$0$ to decimal.

y = 0

$y = 0$

y = 0

$y = 0$

Step 6

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

\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 3 \\ 0 & 0 \\ 1 & - 3 \\ 2 & 0 \end{array}

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 3 \\ 0 & 0 \\ 1 & - 3 \\ 2 & 0 \end{array}$

Step 7

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 & 0 \\ - 1 & 3 \\ 0 & 0 \\ 1 & - 3 \\ 2 & 0 \end{array}

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 3 \\ 0 & 0 \\ 1 & - 3 \\ 2 & 0 \end{array}$

Step 8