Graph f(x)=(x-1)(x^2-9)

$f (x) = (x - 1) (x^{2} - 9)$

Step 1

Find the point at $x = - 1$ .

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

$f (- 1) = {(- 1)}^{3} - 9 \cdot - 1 - {(- 1)}^{2} + 9$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 1 - 9 \cdot - 1 - {(- 1)}^{2} + 9$

Multiply $- 9$ by $- 1$ .

$f (- 1) = - 1 + 9 - {(- 1)}^{2} + 9$

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{2}$ .

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

$f (- 1) = - 1 + 9 + (- 1) {(- 1)}^{2} + 9$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (- 1) = - 1 + 9 + {(- 1)}^{1 + 2} + 9$

Add $1$ and $2$ .

$f (- 1) = - 1 + 9 + {(- 1)}^{3} + 9$

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

$f (- 1) = - 1 + 9 - 1 + 9$

Simplify by adding and subtracting.

Add $- 1$ and $9$ .

$f (- 1) = 8 - 1 + 9$

Subtract $1$ from $8$ .

$f (- 1) = 7 + 9$

Add $7$ and $9$ .

$f (- 1) = 16$

The final answer is $16$ .

$16$

Convert $16$ to decimal.

$y = 16$

Step 2

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} - 9 \cdot 0 - {(0)}^{2} + 9$

Simplify the result.

Simplify each term.

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

$f (0) = 0 - 9 \cdot 0 - {(0)}^{2} + 9$

Multiply $- 9$ by $0$ .

$f (0) = 0 + 0 - {(0)}^{2} + 9$

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

$f (0) = 0 + 0 - 0 + 9$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0 + 0 + 9$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 9$

Add $0$ and $0$ .

$f (0) = 0 + 9$

Add $0$ and $9$ .

$f (0) = 9$

The final answer is $9$ .

$9$

Convert $9$ to decimal.

$y = 9$

Step 3

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} - 9 \cdot 1 - {(1)}^{2} + 9$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 - 9 \cdot 1 - {(1)}^{2} + 9$

Multiply $- 9$ by $1$ .

$f (1) = 1 - 9 - {(1)}^{2} + 9$

One to any power is one.

$f (1) = 1 - 9 - 1 \cdot 1 + 9$

Multiply $- 1$ by $1$ .

$f (1) = 1 - 9 - 1 + 9$

Simplify by adding and subtracting.

Subtract $9$ from $1$ .

$f (1) = - 8 - 1 + 9$

Subtract $1$ from $- 8$ .

$f (1) = - 9 + 9$

Add $- 9$ and $9$ .

$f (1) = 0$

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.

$f (2) = {(2)}^{3} - 9 \cdot 2 - {(2)}^{2} + 9$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - 9 \cdot 2 - {(2)}^{2} + 9$

Multiply $- 9$ by $2$ .

$f (2) = 8 - 18 - {(2)}^{2} + 9$

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

$f (2) = 8 - 18 - 1 \cdot 4 + 9$

Multiply $- 1$ by $4$ .

$f (2) = 8 - 18 - 4 + 9$

Simplify by adding and subtracting.

Subtract $18$ from $8$ .

$f (2) = - 10 - 4 + 9$

Subtract $4$ from $- 10$ .

$f (2) = - 14 + 9$

Add $- 14$ and $9$ .

$f (2) = - 5$

The final answer is $- 5$ .

$- 5$

Convert $- 5$ to decimal.

$y = - 5$

Step 5

Find the point at $x = 3$ .

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

$f (3) = {(3)}^{3} - 9 \cdot 3 - {(3)}^{2} + 9$

Simplify the result.

Simplify each term.

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

$f (3) = 27 - 9 \cdot 3 - {(3)}^{2} + 9$

Multiply $- 9$ by $3$ .

$f (3) = 27 - 27 - {(3)}^{2} + 9$

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

$f (3) = 27 - 27 - 1 \cdot 9 + 9$

Multiply $- 1$ by $9$ .

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

Simplify by adding and subtracting.

Subtract $27$ from $27$ .

$f (3) = 0 - 9 + 9$

Subtract $9$ from $0$ .

$f (3) = - 9 + 9$

Add $- 9$ and $9$ .

$f (3) = 0$

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.

$\begin{array}{c} x & y \\ - 1 & 16 \\ 0 & 9 \\ 1 & 0 \\ 2 & - 5 \\ 3 & 0 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & 16 \\ 0 & 9 \\ 1 & 0 \\ 2 & - 5 \\ 3 & 0 \end{array}$

Step 8

Graph f(x)=(x-1)(x^2-9)

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