Graph f(x)=x^3+x+2

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

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Remove parentheses.

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

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

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

Subtract $2$ from $- 8$ .

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

Add $- 10$ and $2$ .

$f (- 2) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

Remove parentheses.

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

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

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

Subtract $1$ from $- 1$ .

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

Add $- 2$ and $2$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} + 0 + 2$

Simplify the result.

Remove parentheses.

$f (0) = {(0)}^{3} + 0 + 2$

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

$f (0) = 0 + 0 + 2$

Add $0$ and $0$ .

$f (0) = 0 + 2$

Add $0$ and $2$ .

$f (0) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 4

Find the point at $x = 1$ .

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

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

Simplify the result.

Remove parentheses.

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

One to any power is one.

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

Add $1$ and $1$ .

$f (1) = 2 + 2$

Add $2$ and $2$ .

$f (1) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 5

Find the point at $x = 2$ .

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

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

Simplify the result.

Remove parentheses.

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

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

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

Add $8$ and $2$ .

$f (2) = 10 + 2$

Add $10$ and $2$ .

$f (2) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 8 \\ - 1 & 0 \\ 0 & 2 \\ 1 & 4 \\ 2 & 12 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 8 \\ - 1 & 0 \\ 0 & 2 \\ 1 & 4 \\ 2 & 12 \end{array}$

Step 8

Graph f(x)=x^3+x+2

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