Graph x-x^3

$x - x^{3}$

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 1$ by $- 8$ .

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

Add $- 2$ and $8$ .

$f (- 2) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

Add $- 1$ and $1$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 1$ by $8$ .

$f (2) = 2 - 8$

Subtract $8$ from $2$ .

$f (2) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

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

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

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

Rises to the left and falls to the right

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

Graph x-x^3

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