Graph f(x)=(x-1)(x^2-4)

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

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 4$ by $- 1$ .

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

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

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

Simplify by adding and subtracting.

Add $- 1$ and $4$ .

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

Subtract $1$ from $3$ .

$f (- 1) = 2 + 4$

Add $2$ and $4$ .

$f (- 1) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} - 4 \cdot 0 - {(0)}^{2} + 4$

Simplify the result.

Simplify each term.

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

$f (0) = 0 - 4 \cdot 0 - {(0)}^{2} + 4$

Multiply $- 4$ by $0$ .

$f (0) = 0 + 0 - {(0)}^{2} + 4$

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

$f (0) = 0 + 0 - 0 + 4$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0 + 0 + 4$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 4$

Add $0$ and $0$ .

$f (0) = 0 + 4$

Add $0$ and $4$ .

$f (0) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

Multiply $- 4$ by $1$ .

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

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

Simplify by adding and subtracting.

Subtract $4$ from $1$ .

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

Subtract $1$ from $- 3$ .

$f (1) = - 4 + 4$

Add $- 4$ and $4$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 4$ by $3$ .

$f (3) = 27 - 12 - {(3)}^{2} + 4$

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

$f (3) = 27 - 12 - 1 \cdot 9 + 4$

Multiply $- 1$ by $9$ .

$f (3) = 27 - 12 - 9 + 4$

Simplify by adding and subtracting.

Subtract $12$ from $27$ .

$f (3) = 15 - 9 + 4$

Subtract $9$ from $15$ .

$f (3) = 6 + 4$

Add $6$ and $4$ .

$f (3) = 10$

The final answer is $10$ .

$10$

Convert $10$ to decimal.

$y = 10$

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

$\begin{array}{c} x & y \\ - 1 & 6 \\ 0 & 4 \\ 1 & 0 \\ 2 & 0 \\ 3 & 10 \end{array}$

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 1 & 6 \\ 0 & 4 \\ 1 & 0 \\ 2 & 0 \\ 3 & 10 \end{array}$

Graph f(x)=(x-1)(x^2-4)

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