Algebra Examples

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

Step 1

Find the point at $x = - 2$ .

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Step 1.1

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

$f (- 2) = \frac{{(- 2)}^{3}}{8} + 1$

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 $3$ .

$f (- 2) = \frac{- 8}{8} + 1$

Step 1.2.1.2

Divide $- 8$ by $8$ .

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

Step 1.2.2

Add $- 1$ and $1$ .

$f (- 2) = 0$

Step 1.2.3

The final answer is $0$ .

$0$

Step 1.3

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = 0$ .

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Step 2.1

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

$f (0) = \frac{{(0)}^{3}}{8} + 1$

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

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

$f (0) = \frac{0}{8} + 1$

Step 2.2.1.2

Divide $0$ by $8$ .

$f (0) = 0 + 1$

Step 2.2.2

Add $0$ and $1$ .

$f (0) = 1$

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 $x = 2$ .

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Step 3.1

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

$f (2) = \frac{{(2)}^{3}}{8} + 1$

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

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

$f (2) = \frac{8}{8} + 1$

Step 3.2.1.2

Divide $8$ by $8$ .

$f (2) = 1 + 1$

Step 3.2.2

Add $1$ and $1$ .

$f (2) = 2$

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 $x = - 1$ .

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Step 4.1

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

$f (- 1) = \frac{{(- 1)}^{3}}{8} + 1$

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

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

$f (- 1) = \frac{- 1}{8} + 1$

Step 4.2.1.2

Move the negative in front of the fraction.

$f (- 1) = - \frac{1}{8} + 1$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Write $1$ as a fraction with a common denominator.

$f (- 1) = - \frac{1}{8} + \frac{8}{8}$

Step 4.2.2.2

Combine the numerators over the common denominator.

$f (- 1) = \frac{- 1 + 8}{8}$

Step 4.2.2.3

Add $- 1$ and $8$ .

$f (- 1) = \frac{7}{8}$

Step 4.2.3

The final answer is $\frac{7}{8}$ .

$\frac{7}{8}$

Step 4.3

Convert $\frac{7}{8}$ to decimal.

$y = 0.875$

Step 5

Find the point at $x = 1$ .

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Step 5.1

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

$f (1) = \frac{{(1)}^{3}}{8} + 1$

Step 5.2

Simplify the result.

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Step 5.2.1

One to any power is one.

$f (1) = \frac{1}{8} + 1$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Write $1$ as a fraction with a common denominator.

$f (1) = \frac{1}{8} + \frac{8}{8}$

Step 5.2.2.2

Combine the numerators over the common denominator.

$f (1) = \frac{1 + 8}{8}$

Step 5.2.2.3

Add $1$ and $8$ .

$f (1) = \frac{9}{8}$

Step 5.2.3

The final answer is $\frac{9}{8}$ .

$\frac{9}{8}$

Step 5.3

Convert $\frac{9}{8}$ to decimal.

$y = 1.125$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 0.875 \\ 0 & 1 \\ 1 & 1.125 \\ 2 & 2 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 0.875 \\ 0 & 1 \\ 1 & 1.125 \\ 2 & 2 \end{array}$

Step 8