Pre-Algebra Examples

$9 x - x^{3}$

Step 1

Find the point at $x = - 2$ .

Tap for more steps...

Step 1.1

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

$f (- 2) = 9 (- 2) - {(- 2)}^{3}$

Step 1.2

Simplify the result.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply $9$ by $- 2$ .

$f (- 2) = - 18 - {(- 2)}^{3}$

Step 1.2.1.2

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

$f (- 2) = - 18 + 8$

Step 1.2.1.3

Multiply $- 1$ by $- 8$ .

$f (- 2) = - 18 + 8$

Step 1.2.2

Add $- 18$ and $8$ .

$f (- 2) = - 10$

Step 1.2.3

The final answer is $- 10$ .

$- 10$

Step 1.3

Convert $- 10$ to decimal.

$y = - 10$

Step 2

Find the point at $x = - 1$ .

Tap for more steps...

Step 2.1

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

$f (- 1) = 9 (- 1) - {(- 1)}^{3}$

Step 2.2

Simplify the result.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Multiply $9$ by $- 1$ .

$f (- 1) = - 9 - {(- 1)}^{3}$

Step 2.2.1.2

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Tap for more steps...

Step 2.2.1.2.1

Multiply $- 1$ by ${(- 1)}^{3}$ .

Tap for more steps...

Step 2.2.1.2.1.1

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

$f (- 1) = - 9 + (- 1) {(- 1)}^{3}$

Step 2.2.1.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (- 1) = - 9 + {(- 1)}^{1 + 3}$

Step 2.2.1.2.2

Add $1$ and $3$ .

$f (- 1) = - 9 + {(- 1)}^{4}$

Step 2.2.1.3

Raise $- 1$ to the power of $4$ .

$f (- 1) = - 9 + 1$

Step 2.2.2

Add $- 9$ and $1$ .

$f (- 1) = - 8$

Step 2.2.3

The final answer is $- 8$ .

$- 8$

Step 2.3

Convert $- 8$ to decimal.

$y = - 8$

Step 3

Find the point at $x = 0$ .

Tap for more steps...

Step 3.1

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

$f (0) = 9 (0) - {(0)}^{3}$

Step 3.2

Simplify the result.

Tap for more steps...

Step 3.2.1

Simplify each term.

Tap for more steps...

Step 3.2.1.1

Multiply $9$ by $0$ .

$f (0) = 0 - {(0)}^{3}$

Step 3.2.1.2

Raising $0$ to any positive power yields $0$ .

$f (0) = 0 - 0$

Step 3.2.1.3

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0$

Step 3.2.2

Add $0$ and $0$ .

$f (0) = 0$

Step 3.2.3

The final answer is $0$ .

$0$

Step 3.3

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = 1$ .

Tap for more steps...

Step 4.1

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

$f (1) = 9 (1) - {(1)}^{3}$

Step 4.2

Simplify the result.

Tap for more steps...

Step 4.2.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1

Multiply $9$ by $1$ .

$f (1) = 9 - {(1)}^{3}$

Step 4.2.1.2

One to any power is one.

$f (1) = 9 - 1 \cdot 1$

Step 4.2.1.3

Multiply $- 1$ by $1$ .

$f (1) = 9 - 1$

Step 4.2.2

Subtract $1$ from $9$ .

$f (1) = 8$

Step 4.2.3

The final answer is $8$ .

$8$

Step 4.3

Convert $8$ to decimal.

$y = 8$

Step 5

Find the point at $x = 2$ .

Tap for more steps...

Step 5.1

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

$f (2) = 9 (2) - {(2)}^{3}$

Step 5.2

Simplify the result.

Tap for more steps...

Step 5.2.1

Simplify each term.

Tap for more steps...

Step 5.2.1.1

Multiply $9$ by $2$ .

$f (2) = 18 - {(2)}^{3}$

Step 5.2.1.2

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

$f (2) = 18 - 1 \cdot 8$

Step 5.2.1.3

Multiply $- 1$ by $8$ .

$f (2) = 18 - 8$

Step 5.2.2

Subtract $8$ from $18$ .

$f (2) = 10$

Step 5.2.3

The final answer is $10$ .

$10$

Step 5.3

Convert $10$ to decimal.

$y = 10$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 10 \\ - 1 & - 8 \\ 0 & 0 \\ 1 & 8 \\ 2 & 10 \end{array}$

Step 7

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & - 10 \\ - 1 & - 8 \\ 0 & 0 \\ 1 & 8 \\ 2 & 10 \end{array}$

Step 8