Graph f(x)=x(x+1)(x+3)

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

Find the point at $x = - 3$ .

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

$f (- 3) = {(- 3)}^{3} + 4 {(- 3)}^{2} + 3 (- 3)$

Simplify the result.

Simplify each term.

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

$f (- 3) = - 27 + 4 {(- 3)}^{2} + 3 (- 3)$

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

$f (- 3) = - 27 + 4 \cdot 9 + 3 (- 3)$

Multiply $4$ by $9$ .

$f (- 3) = - 27 + 36 + 3 (- 3)$

Multiply $3$ by $- 3$ .

$f (- 3) = - 27 + 36 - 9$

Simplify by adding and subtracting.

Add $- 27$ and $36$ .

$f (- 3) = 9 - 9$

Subtract $9$ from $9$ .

$f (- 3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = - 2$ .

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

$f (- 2) = {(- 2)}^{3} + 4 {(- 2)}^{2} + 3 (- 2)$

Simplify the result.

Simplify each term.

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

$f (- 2) = - 8 + 4 {(- 2)}^{2} + 3 (- 2)$

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

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

Multiply $4$ by $4$ .

$f (- 2) = - 8 + 16 + 3 (- 2)$

Multiply $3$ by $- 2$ .

$f (- 2) = - 8 + 16 - 6$

Simplify by adding and subtracting.

Add $- 8$ and $16$ .

$f (- 2) = 8 - 6$

Subtract $6$ from $8$ .

$f (- 2) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Find the point at $x = - 1$ .

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

$f (- 1) = {(- 1)}^{3} + 4 {(- 1)}^{2} + 3 (- 1)$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 1 + 4 {(- 1)}^{2} + 3 (- 1)$

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

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

Multiply $4$ by $1$ .

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

Multiply $3$ by $- 1$ .

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

Simplify by adding and subtracting.

Add $- 1$ and $4$ .

$f (- 1) = 3 - 3$

Subtract $3$ from $3$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} + 4 {(1)}^{2} + 3 (1)$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 + 4 {(1)}^{2} + 3 (1)$

One to any power is one.

$f (1) = 1 + 4 \cdot 1 + 3 (1)$

Multiply $4$ by $1$ .

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

Multiply $3$ by $1$ .

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

Simplify by adding numbers.

Add $1$ and $4$ .

$f (1) = 5 + 3$

Add $5$ and $3$ .

$f (1) = 8$

The final answer is $8$ .

$8$

Convert $8$ to decimal.

$y = 8$

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

$\begin{array}{c} x & y \\ - 3 & 0 \\ - 2 & 2 \\ - 1 & 0 \\ 0 & 0 \\ 1 & 8 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 3 & 0 \\ - 2 & 2 \\ - 1 & 0 \\ 0 & 0 \\ 1 & 8 \end{array}$

Graph f(x)=x(x+1)(x+3)

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