Algebra Examples

$x^{3} - 4$

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

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

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

Subtract $4$ from $- 8$ .

$f (- 2) = - 12$

The final answer is $- 12$ .

$- 12$

Convert $- 12$ to decimal.

$y = - 12$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

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

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

Subtract $4$ from $- 1$ .

$f (- 1) = - 5$

The final answer is $- 5$ .

$- 5$

Convert $- 5$ to decimal.

$y = - 5$

Step 3

Find the point at $x = 0$ .

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

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

Simplify the result.

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

$f (0) = 0 - 4$

Subtract $4$ from $0$ .

$f (0) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Step 4

Find the point at $x = 1$ .

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

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

Simplify the result.

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One to any power is one.

$f (1) = 1 - 4$

Subtract $4$ from $1$ .

$f (1) = - 3$

The final answer is $- 3$ .

$- 3$

Convert $- 3$ to decimal.

$y = - 3$

Step 5

Find the point at $x = 2$ .

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

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

Simplify the result.

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

$f (2) = 8 - 4$

Subtract $4$ from $8$ .

$f (2) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 12 \\ - 1 & - 5 \\ 0 & - 4 \\ 1 & - 3 \\ 2 & 4 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 12 \\ - 1 & - 5 \\ 0 & - 4 \\ 1 & - 3 \\ 2 & 4 \end{array}$

Step 8