Algebra Examples

$x^{3} + x + 1$

Step 1

Find the point at $x = - 2$ .

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Step 1.1

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

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

Step 1.2

Simplify the result.

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Step 1.2.1

Remove parentheses.

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

Step 1.2.2

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

$f (- 2) = - 8 - 2 + 1$

Step 1.2.3

Subtract $2$ from $- 8$ .

$f (- 2) = - 10 + 1$

Step 1.2.4

Add $- 10$ and $1$ .

$f (- 2) = - 9$

Step 1.2.5

The final answer is $- 9$ .

$- 9$

Step 1.3

Convert $- 9$ to decimal.

$y = - 9$

Step 2

Find the point at $x = - 1$ .

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Step 2.1

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

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

Step 2.2

Simplify the result.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

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

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

Step 2.2.3

Subtract $1$ from $- 1$ .

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

Step 2.2.4

Add $- 2$ and $1$ .

$f (- 1) = - 1$

Step 2.2.5

The final answer is $- 1$ .

$- 1$

Step 2.3

Convert $- 1$ to decimal.

$y = - 1$

Step 3

Find the point at $x = 0$ .

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Step 3.1

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

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

Step 3.2

Simplify the result.

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Step 3.2.1

Remove parentheses.

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

Step 3.2.2

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

$f (0) = 0 + 0 + 1$

Step 3.2.3

Add $0$ and $0$ .

$f (0) = 0 + 1$

Step 3.2.4

Add $0$ and $1$ .

$f (0) = 1$

Step 3.2.5

The final answer is $1$ .

$1$

Step 3.3

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

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

Step 4.2

Simplify the result.

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Step 4.2.1

Remove parentheses.

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

Step 4.2.2

One to any power is one.

$f (1) = 1 + 1 + 1$

Step 4.2.3

Add $1$ and $1$ .

$f (1) = 2 + 1$

Step 4.2.4

Add $2$ and $1$ .

$f (1) = 3$

Step 4.2.5

The final answer is $3$ .

$3$

Step 4.3

Convert $3$ to decimal.

$y = 3$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

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

Step 5.2

Simplify the result.

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Step 5.2.1

Remove parentheses.

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

Step 5.2.2

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

$f (2) = 8 + 2 + 1$

Step 5.2.3

Add $8$ and $2$ .

$f (2) = 10 + 1$

Step 5.2.4

Add $10$ and $1$ .

$f (2) = 11$

Step 5.2.5

The final answer is $11$ .

$11$

Step 5.3

Convert $11$ to decimal.

$y = 11$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 9 \\ - 1 & - 1 \\ 0 & 1 \\ 1 & 3 \\ 2 & 11 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 9 \\ - 1 & - 1 \\ 0 & 1 \\ 1 & 3 \\ 2 & 11 \end{array}$

Step 8