Graph x^3-3x^2-x+3

$x^{3} - 3 x^{2} - x + 3$

Step 1

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (- 1) = - 1 - 3 \cdot 1 - (- 1) + 3$

Multiply $- 3$ by $1$ .

$f (- 1) = - 1 - 3 - (- 1) + 3$

Multiply $- 1$ by $- 1$ .

$f (- 1) = - 1 - 3 + 1 + 3$

Simplify by adding and subtracting.

Subtract $3$ from $- 1$ .

$f (- 1) = - 4 + 1 + 3$

Add $- 4$ and $1$ .

$f (- 1) = - 3 + 3$

Add $- 3$ and $3$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (0) = 0 - 3 \cdot 0 - (0) + 3$

Multiply $- 3$ by $0$ .

$f (0) = 0 + 0 - (0) + 3$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0 + 0 + 3$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 3$

Add $0$ and $0$ .

$f (0) = 0 + 3$

Add $0$ and $3$ .

$f (0) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Step 3

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

One to any power is one.

$f (1) = 1 - 3 \cdot 1 - (1) + 3$

Multiply $- 3$ by $1$ .

$f (1) = 1 - 3 - (1) + 3$

Multiply $- 1$ by $1$ .

$f (1) = 1 - 3 - 1 + 3$

Simplify by adding and subtracting.

Subtract $3$ from $1$ .

$f (1) = - 2 - 1 + 3$

Subtract $1$ from $- 2$ .

$f (1) = - 3 + 3$

Add $- 3$ and $3$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

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

$f (2) = 8 - 3 \cdot 4 - (2) + 3$

Multiply $- 3$ by $4$ .

$f (2) = 8 - 12 - (2) + 3$

Multiply $- 1$ by $2$ .

$f (2) = 8 - 12 - 2 + 3$

Simplify by adding and subtracting.

Subtract $12$ from $8$ .

$f (2) = - 4 - 2 + 3$

Subtract $2$ from $- 4$ .

$f (2) = - 6 + 3$

Add $- 6$ and $3$ .

$f (2) = - 3$

The final answer is $- 3$ .

$- 3$

Convert $- 3$ to decimal.

$y = - 3$

Step 5

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

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

Simplify the result.

Simplify each term.

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

$f (3) = 27 - 3 {(3)}^{2} - (3) + 3$

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

$f (3) = 27 - 3 \cdot 9 - (3) + 3$

Multiply $- 3$ by $9$ .

$f (3) = 27 - 27 - (3) + 3$

Multiply $- 1$ by $3$ .

$f (3) = 27 - 27 - 3 + 3$

Simplify by adding and subtracting.

Subtract $27$ from $27$ .

$f (3) = 0 - 3 + 3$

Subtract $3$ from $0$ .

$f (3) = - 3 + 3$

Add $- 3$ and $3$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 6

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

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

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

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

Step 8

Graph x^3-3x^2-x+3

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