Algebra Examples

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

Step 1

Find the point at $x = 0$ .

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Step 1.1

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

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

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify the numerator.

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Step 1.2.1.1

Subtract $2$ from $0$ .

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

Step 1.2.1.2

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

$f (0) = \frac{- 8}{2}$

Step 1.2.2

Divide $- 8$ by $2$ .

$f (0) = - 4$

Step 1.2.3

The final answer is $- 4$ .

$- 4$

Step 1.3

Convert $- 4$ to decimal.

$y = - 4$

Step 2

Find the point at $x = 2$ .

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Step 2.1

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

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

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify the numerator.

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Step 2.2.1.1

Subtract $2$ from $2$ .

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

Step 2.2.1.2

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

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

Step 2.2.2

Divide $0$ by $2$ .

$f (2) = 0$

Step 2.2.3

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 4$ .

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Step 3.1

Replace the variable $x$ with $4$ in the expression.

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

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify the numerator.

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Step 3.2.1.1

Subtract $2$ from $4$ .

$f (4) = \frac{2^{3}}{2}$

Step 3.2.1.2

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

$f (4) = \frac{8}{2}$

Step 3.2.2

Divide $8$ by $2$ .

$f (4) = 4$

Step 3.2.3

The final answer is $4$ .

$4$

Step 3.3

Convert $4$ to decimal.

$y = 4$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

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

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Subtract $2$ from $1$ .

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

Step 4.2.1.2

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

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

Step 4.2.2

Move the negative in front of the fraction.

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

Step 4.2.3

The final answer is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Step 4.3

Convert $- \frac{1}{2}$ to decimal.

$y = - 0.5$

Step 5

Find the point at $x = 3$ .

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Step 5.1

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

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

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify the numerator.

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Step 5.2.1.1

Subtract $2$ from $3$ .

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

Step 5.2.1.2

One to any power is one.

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

Step 5.2.2

The final answer is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 5.3

Convert $\frac{1}{2}$ to decimal.

$y = 0.5$

Step 6

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

$\begin{array}{c} x & y \\ 0 & - 4 \\ 1 & - 0.5 \\ 2 & 0 \\ 3 & 0.5 \\ 4 & 4 \end{array}$

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

$\begin{array}{c} x & y \\ 0 & - 4 \\ 1 & - 0.5 \\ 2 & 0 \\ 3 & 0.5 \\ 4 & 4 \end{array}$

Step 8