Pre-Algebra Examples

${(x - 7)}^{3}$

Step 1

Find the point at $x = 5$ .

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Step 1.1

Replace the variable $x$ with $5$ in the expression.

$f (5) = {((5) - 7)}^{3}$

Step 1.2

Simplify the result.

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Step 1.2.1

Subtract $7$ from $5$ .

$f (5) = {(- 2)}^{3}$

Step 1.2.2

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

$f (5) = - 8$

Step 1.2.3

The final answer is $- 8$ .

$- 8$

Step 1.3

Convert $- 8$ to decimal.

$y = - 8$

Step 2

Find the point at $x = 6$ .

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Step 2.1

Replace the variable $x$ with $6$ in the expression.

$f (6) = {((6) - 7)}^{3}$

Step 2.2

Simplify the result.

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Step 2.2.1

Subtract $7$ from $6$ .

$f (6) = {(- 1)}^{3}$

Step 2.2.2

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

$f (6) = - 1$

Step 2.2.3

The final answer is $- 1$ .

$- 1$

Step 2.3

Convert $- 1$ to decimal.

$y = - 1$

Step 3

Find the point at $x = 7$ .

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Step 3.1

Replace the variable $x$ with $7$ in the expression.

$f (7) = {((7) - 7)}^{3}$

Step 3.2

Simplify the result.

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Step 3.2.1

Subtract $7$ from $7$ .

$f (7) = 0^{3}$

Step 3.2.2

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

$f (7) = 0$

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 $x = 8$ .

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Step 4.1

Replace the variable $x$ with $8$ in the expression.

$f (8) = {((8) - 7)}^{3}$

Step 4.2

Simplify the result.

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Step 4.2.1

Subtract $7$ from $8$ .

$f (8) = 1^{3}$

Step 4.2.2

One to any power is one.

$f (8) = 1$

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 $x = 9$ .

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Step 5.1

Replace the variable $x$ with $9$ in the expression.

$f (9) = {((9) - 7)}^{3}$

Step 5.2

Simplify the result.

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Step 5.2.1

Subtract $7$ from $9$ .

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

Step 5.2.2

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

$f (9) = 8$

Step 5.2.3

The final answer is $8$ .

$8$

Step 5.3

Convert $8$ to decimal.

$y = 8$

Step 6

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

$\begin{array}{c} x & y \\ 5 & - 8 \\ 6 & - 1 \\ 7 & 0 \\ 8 & 1 \\ 9 & 8 \end{array}$

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

$\begin{array}{c} x & y \\ 5 & - 8 \\ 6 & - 1 \\ 7 & 0 \\ 8 & 1 \\ 9 & 8 \end{array}$

Step 8