Algebra Examples

y = - \frac{3}{2} x^{3}

$y = - \frac{3}{2} x^{3}$

Step 1

Find the point at

x = - 2

$x = - 2$ .

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Step 1.1

Replace the variable

x

$x$ with

- 2

$- 2$ in the expression.

f (- 2) = - \frac{3 {(- 2)}^{3}}{2}

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

Step 1.2

Simplify the result.

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Step 1.2.1

Cancel the common factor of

{(- 2)}^{3}

${(- 2)}^{3}$ and

2

$2$ .

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Step 1.2.1.1

Rewrite

- 2

$- 2$ as

- 1 (2)

$- 1 (2)$ .

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

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

Step 1.2.1.2

Apply the product rule to

- 1 (2)

$- 1 (2)$ .

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

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

Step 1.2.1.3

Raise

- 1

$- 1$ to the power of

3

$3$ .

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

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

Step 1.2.1.4

Factor

2

$2$ out of

3 (- 1 \cdot 2^{3})

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

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

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

Step 1.2.1.5

Cancel the common factors.

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Step 1.2.1.5.1

Factor

2

$2$ out of

2

$2$ .

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

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

Step 1.2.1.5.2

Cancel the common factor.

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

Step 1.2.1.5.3

Rewrite the expression.

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

Step 1.2.1.5.4

Divide

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

$1$ .

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

Step 1.2.2

Raise

$2$ to the power of

$2$ .

$f (- 2) = - (3 (- 1 \cdot 4))$

Step 1.2.3

Multiply

$- (3 (- 1 \cdot 4))$ .

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Step 1.2.3.1

Multiply

$- 1$ by

$4$ .

$f (- 2) = - (3 \cdot - 4)$

Step 1.2.3.2

Multiply

$3$ by

$- 4$ .

$f (- 2) = 12$

Step 1.2.3.3

Multiply

$- 1$ by

$- 12$ .

$f (- 2) = 12$

Step 1.2.4

The final answer is

$12$ .

$12$

Step 1.3

Convert

$12$ to decimal.

$y = 12$

Step 2

Find the point at

$x = 0$ .

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Step 2.1

Replace the variable

$x$ with

$0$ in the expression.

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

Step 2.2

Simplify the result.

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Step 2.2.1

Raising

$0$ to any positive power yields

$0$ .

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

Step 2.2.2

Multiply

$3$ by

$0$ .

$f (0) = - \frac{0}{2}$

Step 2.2.3

Divide

$0$ by

$2$ .

$f (0) = - 0$

Step 2.2.4

Multiply

$- 1$ by

$0$ .

$f (0) = 0$

Step 2.2.5

The final answer is

$0$ .

$0$

Step 2.3

Convert

$0$ to decimal.

$y = 0$

Step 3

Find the point at

$x = 2$ .

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Step 3.1

Replace the variable

$x$ with

$2$ in the expression.

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

Step 3.2

Simplify the result.

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Step 3.2.1

Cancel the common factor of

${(2)}^{3}$ and

$2$ .

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Step 3.2.1.1

Factor

$2$ out of

$3 {(2)}^{3}$ .

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

Step 3.2.1.2

Cancel the common factors.

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Step 3.2.1.2.1

Factor

$2$ out of

$2$ .

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

Step 3.2.1.2.2

Cancel the common factor.

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

Step 3.2.1.2.3

Rewrite the expression.

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

Step 3.2.1.2.4

Divide

$3 \cdot 2^{2}$ by

$1$ .

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

Step 3.2.2

Raise

$2$ to the power of

$2$ .

$f (2) = - (3 \cdot 4)$

Step 3.2.3

Multiply

$- (3 \cdot 4)$ .

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Step 3.2.3.1

Multiply

$3$ by

$4$ .

$f (2) = - 1 \cdot 12$

Step 3.2.3.2

Multiply

$- 1$ by

$12$ .

$f (2) = - 12$

Step 3.2.4

The final answer is

$- 12$ .

$- 12$

Step 3.3

Convert

$- 12$ to decimal.

$y = - 12$

Step 4

Find the point at

$x = - 1$ .

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Step 4.1

Replace the variable

$x$ with

$- 1$ in the expression.

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

Step 4.2

Simplify the result.

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Step 4.2.1

Raise

$- 1$ to the power of

$3$ .

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

Step 4.2.2

Multiply

$3$ by

$- 1$ .

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

Step 4.2.3

Move the negative in front of the fraction.

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

Step 4.2.4

The final answer is

$\frac{3}{2}$ .

$\frac{3}{2}$

Step 4.3

Convert

$\frac{3}{2}$ to decimal.

$y = 1.5$

Step 5

Find the point at

$x = 1$ .

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Step 5.1

Replace the variable

$x$ with

$1$ in the expression.

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

Step 5.2

Simplify the result.

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Step 5.2.1

One to any power is one.

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

Step 5.2.2

Multiply

$3$ by

$1$ .

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

Step 5.2.3

The final answer is

$- \frac{3}{2}$ .

$- \frac{3}{2}$

Step 5.3

Convert

$- \frac{3}{2}$ to decimal.

$y = - 1.5$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & 1.5 \\ 0 & 0 \\ 1 & - 1.5 \\ 2 & - 12 \end{array}$

Step 7

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & 1.5 \\ 0 & 0 \\ 1 & - 1.5 \\ 2 & - 12 \end{array}$

Step 8