Graph f(x)=x^3+x^2-x-1

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

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (- 2) = - 8 + 4 - (- 2) - 1$

Multiply $- 1$ by $- 2$ .

$f (- 2) = - 8 + 4 + 2 - 1$

Simplify by adding and subtracting.

Add $- 8$ and $4$ .

$f (- 2) = - 4 + 2 - 1$

Add $- 4$ and $2$ .

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

Subtract $1$ from $- 2$ .

$f (- 2) = - 3$

The final answer is $- 3$ .

$- 3$

Convert $- 3$ to decimal.

$y = - 3$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Raise $- 1$ to the power of $2$ .

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

Multiply $- 1$ by $- 1$ .

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

Simplify by adding and subtracting.

Add $- 1$ and $1$ .

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

Add $0$ and $1$ .

$f (- 1) = 1 - 1$

Subtract $1$ from $1$ .

$f (- 1) = 0$

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.

$f (0) = {(0)}^{3} + {(0)}^{2} - (0) - 1$

Simplify the result.

Simplify each term.

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

$f (0) = 0 + {(0)}^{2} - (0) - 1$

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

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

Multiply $- 1$ by $0$ .

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

Simplify by adding and subtracting.

Add $0$ and $0$ .

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

Add $0$ and $0$ .

$f (0) = 0 - 1$

Subtract $1$ from $0$ .

$f (0) = - 1$

The final answer is $- 1$ .

$- 1$

Convert $- 1$ to decimal.

$y = - 1$

Step 4

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

Simplify by adding and subtracting.

Add $1$ and $1$ .

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

Subtract $1$ from $2$ .

$f (1) = 1 - 1$

Subtract $1$ from $1$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 5

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (2) = 8 + 4 - (2) - 1$

Multiply $- 1$ by $2$ .

$f (2) = 8 + 4 - 2 - 1$

Simplify by adding and subtracting.

Add $8$ and $4$ .

$f (2) = 12 - 2 - 1$

Subtract $2$ from $12$ .

$f (2) = 10 - 1$

Subtract $1$ from $10$ .

$f (2) = 9$

The final answer is $9$ .

$9$

Convert $9$ to decimal.

$y = 9$

Step 6

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

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

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

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

Step 8

Graph f(x)=x^3+x^2-x-1

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