Pre-Algebra Examples

$64 x^{3} - 125$

Step 1

Find the point at $x = - 2$ .

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Step 1.1

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

$f (- 2) = 64 {(- 2)}^{3} - 125$

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

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

$f (- 2) = 64 \cdot - 8 - 125$

Step 1.2.1.2

Multiply $64$ by $- 8$ .

$f (- 2) = - 512 - 125$

Step 1.2.2

Subtract $125$ from $- 512$ .

$f (- 2) = - 637$

Step 1.2.3

The final answer is $- 637$ .

$- 637$

Step 1.3

Convert $- 637$ to decimal.

$y = - 637$

Step 2

Find the point at $x = - 1$ .

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Step 2.1

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

$f (- 1) = 64 {(- 1)}^{3} - 125$

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

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

$f (- 1) = 64 \cdot - 1 - 125$

Step 2.2.1.2

Multiply $64$ by $- 1$ .

$f (- 1) = - 64 - 125$

Step 2.2.2

Subtract $125$ from $- 64$ .

$f (- 1) = - 189$

Step 2.2.3

The final answer is $- 189$ .

$- 189$

Step 2.3

Convert $- 189$ to decimal.

$y = - 189$

Step 3

Find the point at $x = 0$ .

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Step 3.1

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

$f (0) = 64 {(0)}^{3} - 125$

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

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

$f (0) = 64 \cdot 0 - 125$

Step 3.2.1.2

Multiply $64$ by $0$ .

$f (0) = 0 - 125$

Step 3.2.2

Subtract $125$ from $0$ .

$f (0) = - 125$

Step 3.2.3

The final answer is $- 125$ .

$- 125$

Step 3.3

Convert $- 125$ to decimal.

$y = - 125$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

$f (1) = 64 {(1)}^{3} - 125$

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

One to any power is one.

$f (1) = 64 \cdot 1 - 125$

Step 4.2.1.2

Multiply $64$ by $1$ .

$f (1) = 64 - 125$

Step 4.2.2

Subtract $125$ from $64$ .

$f (1) = - 61$

Step 4.2.3

The final answer is $- 61$ .

$- 61$

Step 4.3

Convert $- 61$ to decimal.

$y = - 61$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

$f (2) = 64 {(2)}^{3} - 125$

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

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

$f (2) = 64 \cdot 8 - 125$

Step 5.2.1.2

Multiply $64$ by $8$ .

$f (2) = 512 - 125$

Step 5.2.2

Subtract $125$ from $512$ .

$f (2) = 387$

Step 5.2.3

The final answer is $387$ .

$387$

Step 5.3

Convert $387$ to decimal.

$y = 387$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 637 \\ - 1 & - 189 \\ 0 & - 125 \\ 1 & - 61 \\ 2 & 387 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 637 \\ - 1 & - 189 \\ 0 & - 125 \\ 1 & - 61 \\ 2 & 387 \end{array}$

Step 8