Graph f(x)=(x+1)(x^2-16)

$f (x) = (x + 1) (x^{2} - 16)$

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = {(- 2)}^{3} - 16 \cdot - 2 + {(- 2)}^{2} - 16$

Simplify the result.

Simplify each term.

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

$f (- 2) = - 8 - 16 \cdot - 2 + {(- 2)}^{2} - 16$

Multiply $- 16$ by $- 2$ .

$f (- 2) = - 8 + 32 + {(- 2)}^{2} - 16$

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

$f (- 2) = - 8 + 32 + 4 - 16$

Simplify by adding and subtracting.

Add $- 8$ and $32$ .

$f (- 2) = 24 + 4 - 16$

Add $24$ and $4$ .

$f (- 2) = 28 - 16$

Subtract $16$ from $28$ .

$f (- 2) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = {(- 1)}^{3} - 16 \cdot - 1 + {(- 1)}^{2} - 16$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 1 - 16 \cdot - 1 + {(- 1)}^{2} - 16$

Multiply $- 16$ by $- 1$ .

$f (- 1) = - 1 + 16 + {(- 1)}^{2} - 16$

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

$f (- 1) = - 1 + 16 + 1 - 16$

Simplify by adding and subtracting.

Add $- 1$ and $16$ .

$f (- 1) = 15 + 1 - 16$

Add $15$ and $1$ .

$f (- 1) = 16 - 16$

Subtract $16$ from $16$ .

$f (- 1) = 0$

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.

$f (0) = {(0)}^{3} - 16 \cdot 0 + {(0)}^{2} - 16$

Simplify the result.

Simplify each term.

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

$f (0) = 0 - 16 \cdot 0 + {(0)}^{2} - 16$

Multiply $- 16$ by $0$ .

$f (0) = 0 + 0 + {(0)}^{2} - 16$

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

$f (0) = 0 + 0 + 0 - 16$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 + 0 - 16$

Add $0$ and $0$ .

$f (0) = 0 - 16$

Subtract $16$ from $0$ .

$f (0) = - 16$

The final answer is $- 16$ .

$- 16$

Convert $- 16$ to decimal.

$y = - 16$

Step 4

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} - 16 \cdot 1 + {(1)}^{2} - 16$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 - 16 \cdot 1 + {(1)}^{2} - 16$

Multiply $- 16$ by $1$ .

$f (1) = 1 - 16 + {(1)}^{2} - 16$

One to any power is one.

$f (1) = 1 - 16 + 1 - 16$

Simplify by adding and subtracting.

Subtract $16$ from $1$ .

$f (1) = - 15 + 1 - 16$

Add $- 15$ and $1$ .

$f (1) = - 14 - 16$

Subtract $16$ from $- 14$ .

$f (1) = - 30$

The final answer is $- 30$ .

$- 30$

Convert $- 30$ to decimal.

$y = - 30$

Step 5

Find the point at $x = 2$ .

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

$f (2) = {(2)}^{3} - 16 \cdot 2 + {(2)}^{2} - 16$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - 16 \cdot 2 + {(2)}^{2} - 16$

Multiply $- 16$ by $2$ .

$f (2) = 8 - 32 + {(2)}^{2} - 16$

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

$f (2) = 8 - 32 + 4 - 16$

Simplify by adding and subtracting.

Subtract $32$ from $8$ .

$f (2) = - 24 + 4 - 16$

Add $- 24$ and $4$ .

$f (2) = - 20 - 16$

Subtract $16$ from $- 20$ .

$f (2) = - 36$

The final answer is $- 36$ .

$- 36$

Convert $- 36$ to decimal.

$y = - 36$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & 0 \\ 0 & - 16 \\ 1 & - 30 \\ 2 & - 36 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & 0 \\ 0 & - 16 \\ 1 & - 30 \\ 2 & - 36 \end{array}$

Step 8

Graph f(x)=(x+1)(x^2-16)

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