Graph y=x+x^3

$y = x + x^{3}$

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

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

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

Subtract $8$ from $- 2$ .

$f (- 2) = - 10$

The final answer is $- 10$ .

$- 10$

Convert $- 10$ to decimal.

$y = - 10$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

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

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

Subtract $1$ from $- 1$ .

$f (- 1) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Step 3

Find the point at $x = 0$ .

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

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

Simplify the result.

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

$f (0) = 0 + 0$

Add $0$ and $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = 1$ .

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

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

Simplify the result.

One to any power is one.

$f (1) = 1 + 1$

Add $1$ and $1$ .

$f (1) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 5

Find the point at $x = 2$ .

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

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

Simplify the result.

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

$f (2) = 2 + 8$

Add $2$ and $8$ .

$f (2) = 10$

The final answer is $10$ .

$10$

Convert $10$ to decimal.

$y = 10$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 10 \\ - 1 & - 2 \\ 0 & 0 \\ 1 & 2 \\ 2 & 10 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 10 \\ - 1 & - 2 \\ 0 & 0 \\ 1 & 2 \\ 2 & 10 \end{array}$

Step 8

Graph y=x+x^3

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