Pre-Algebra Examples

$3 {(x - 1)}^{3} - 2$

Step 1

Find the point at $x = - 1$ .

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Step 1.1

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

$f (- 1) = 3 {((- 1) - 1)}^{3} - 2$

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

Subtract $1$ from $- 1$ .

$f (- 1) = 3 {(- 2)}^{3} - 2$

Step 1.2.1.2

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

$f (- 1) = 3 \cdot - 8 - 2$

Step 1.2.1.3

Multiply $3$ by $- 8$ .

$f (- 1) = - 24 - 2$

Step 1.2.2

Subtract $2$ from $- 24$ .

$f (- 1) = - 26$

Step 1.2.3

The final answer is $- 26$ .

$- 26$

Step 1.3

Convert $- 26$ to decimal.

$y = - 26$

Step 2

Find the point at $x = 0$ .

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Step 2.1

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

$f (0) = 3 {((0) - 1)}^{3} - 2$

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

Subtract $1$ from $0$ .

$f (0) = 3 {(- 1)}^{3} - 2$

Step 2.2.1.2

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

$f (0) = 3 \cdot - 1 - 2$

Step 2.2.1.3

Multiply $3$ by $- 1$ .

$f (0) = - 3 - 2$

Step 2.2.2

Subtract $2$ from $- 3$ .

$f (0) = - 5$

Step 2.2.3

The final answer is $- 5$ .

$- 5$

Step 2.3

Convert $- 5$ to decimal.

$y = - 5$

Step 3

Find the point at $x = 1$ .

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Step 3.1

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

$f (1) = 3 {((1) - 1)}^{3} - 2$

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

Subtract $1$ from $1$ .

$f (1) = 3 \cdot 0^{3} - 2$

Step 3.2.1.2

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

$f (1) = 3 \cdot 0 - 2$

Step 3.2.1.3

Multiply $3$ by $0$ .

$f (1) = 0 - 2$

Step 3.2.2

Subtract $2$ from $0$ .

$f (1) = - 2$

Step 3.2.3

The final answer is $- 2$ .

$- 2$

Step 3.3

Convert $- 2$ to decimal.

$y = - 2$

Step 4

Find the point at $x = 2$ .

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Step 4.1

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

$f (2) = 3 {((2) - 1)}^{3} - 2$

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

Subtract $1$ from $2$ .

$f (2) = 3 \cdot 1^{3} - 2$

Step 4.2.1.2

One to any power is one.

$f (2) = 3 \cdot 1 - 2$

Step 4.2.1.3

Multiply $3$ by $1$ .

$f (2) = 3 - 2$

Step 4.2.2

Subtract $2$ from $3$ .

$f (2) = 1$

Step 4.2.3

The final answer is $1$ .

$1$

Step 4.3

Convert $1$ to decimal.

$y = 1$

Step 5

Find the point at $x = 3$ .

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Step 5.1

Replace the variable $x$ with $3$ in the expression.

$f (3) = 3 {((3) - 1)}^{3} - 2$

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

Subtract $1$ from $3$ .

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

Step 5.2.1.2

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

$f (3) = 3 \cdot 8 - 2$

Step 5.2.1.3

Multiply $3$ by $8$ .

$f (3) = 24 - 2$

Step 5.2.2

Subtract $2$ from $24$ .

$f (3) = 22$

Step 5.2.3

The final answer is $22$ .

$22$

Step 5.3

Convert $22$ to decimal.

$y = 22$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & - 26 \\ 0 & - 5 \\ 1 & - 2 \\ 2 & 1 \\ 3 & 22 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & - 26 \\ 0 & - 5 \\ 1 & - 2 \\ 2 & 1 \\ 3 & 22 \end{array}$

Step 8