Graph f(x)=1/8(x+4)(x+2)(x-2)

$f (x) = \frac{1}{8} (x + 4) (x + 2) (x - 2)$

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Combine fractions.

Combine the numerators over the common denominator.

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

Simplify the expression.

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

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

Add $4$ and $2$ .

$f (- 2) = - 2 + \frac{{(- 2)}^{3}}{8} + \frac{6}{2}$

Simplify each term.

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

$f (- 2) = - 2 + \frac{- 8}{8} + \frac{6}{2}$

Divide $- 8$ by $8$ .

$f (- 2) = - 2 - 1 + \frac{6}{2}$

Divide $6$ by $2$ .

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

Simplify by adding and subtracting.

Subtract $1$ from $- 2$ .

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

Add $- 3$ and $3$ .

$f (- 2) = 0$

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.

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2}}{2} - \frac{0}{2} - 2$

Simplify the result.

Find the common denominator.

Multiply $\frac{{(0)}^{2}}{2}$ by $\frac{4}{4}$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2}}{2} \cdot \frac{4}{4} - \frac{0}{2} - 2$

Multiply $\frac{{(0)}^{2}}{2}$ by $\frac{4}{4}$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{2 \cdot 4} - \frac{0}{2} - 2$

Multiply $\frac{0}{2}$ by $\frac{4}{4}$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{2 \cdot 4} - (\frac{0}{2} \cdot \frac{4}{4}) - 2$

Multiply $\frac{0}{2}$ by $\frac{4}{4}$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{2 \cdot 4} - \frac{0 \cdot 4}{2 \cdot 4} - 2$

Write $- 2$ as a fraction with denominator $1$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{2 \cdot 4} - \frac{0 \cdot 4}{2 \cdot 4} + \frac{- 2}{1}$

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{2 \cdot 4} - \frac{0 \cdot 4}{2 \cdot 4} + \frac{- 2}{1} \cdot \frac{8}{8}$

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{2 \cdot 4} - \frac{0 \cdot 4}{2 \cdot 4} + \frac{- 2 \cdot 8}{8}$

Multiply $2$ by $4$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{8} - \frac{0 \cdot 4}{2 \cdot 4} + \frac{- 2 \cdot 8}{8}$

Multiply $2$ by $4$ .

$f (0) = \frac{{(0)}^{3}}{8} + \frac{{(0)}^{2} \cdot 4}{8} - \frac{0 \cdot 4}{8} + \frac{- 2 \cdot 8}{8}$

Combine the numerators over the common denominator.

$f (0) = \frac{{(0)}^{3} + {(0)}^{2} \cdot 4 + 0 \cdot 4 - 2 \cdot 8}{8}$

Simplify each term.

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

$f (0) = \frac{{(0)}^{3} + 0 \cdot 4 + 0 \cdot 4 - 2 \cdot 8}{8}$

Multiply $0$ by $4$ .

$f (0) = \frac{{(0)}^{3} + 0 + 0 \cdot 4 - 2 \cdot 8}{8}$

Multiply $0$ by $4$ .

$f (0) = \frac{{(0)}^{3} + 0 + 0 - 2 \cdot 8}{8}$

Multiply $- 2$ by $8$ .

$f (0) = \frac{{(0)}^{3} + 0 + 0 - 16}{8}$

Simplify the expression.

Add ${(0)}^{3}$ and $0$ .

$f (0) = \frac{{(0)}^{3} + 0 - 16}{8}$

Add ${(0)}^{3}$ and $0$ .

$f (0) = \frac{{(0)}^{3} - 16}{8}$

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

$f (0) = \frac{0 - 16}{8}$

Subtract $16$ from $0$ .

$f (0) = \frac{- 16}{8}$

Divide $- 16$ by $8$ .

$f (0) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Step 3

Find the point at $x = 2$ .

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

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

Simplify the result.

Combine fractions.

Combine the numerators over the common denominator.

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

Simplify the expression.

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

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

Subtract $2$ from $4$ .

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

Simplify each term.

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

$f (2) = - 2 + \frac{8}{8} + \frac{2}{2}$

Divide $8$ by $8$ .

$f (2) = - 2 + 1 + \frac{2}{2}$

Divide $2$ by $2$ .

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

Simplify by adding numbers.

Add $- 2$ and $1$ .

$f (2) = - 1 + 1$

Add $- 1$ and $1$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = - 3$ .

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

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

Simplify the result.

Combine fractions.

Combine the numerators over the common denominator.

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

Simplify the expression.

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

$f (- 3) = - 2 + \frac{{(- 3)}^{3}}{8} + \frac{9 + 3}{2}$

Add $9$ and $3$ .

$f (- 3) = - 2 + \frac{{(- 3)}^{3}}{8} + \frac{12}{2}$

Simplify each term.

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

$f (- 3) = - 2 + \frac{- 27}{8} + \frac{12}{2}$

Move the negative in front of the fraction.

$f (- 3) = - 2 - \frac{27}{8} + \frac{12}{2}$

Divide $12$ by $2$ .

$f (- 3) = - 2 - \frac{27}{8} + 6$

Find the common denominator.

Write $- 2$ as a fraction with denominator $1$ .

$f (- 3) = \frac{- 2}{1} - \frac{27}{8} + 6$

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$f (- 3) = \frac{- 2}{1} \cdot \frac{8}{8} - \frac{27}{8} + 6$

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$f (- 3) = \frac{- 2 \cdot 8}{8} - \frac{27}{8} + 6$

Write $6$ as a fraction with denominator $1$ .

$f (- 3) = \frac{- 2 \cdot 8}{8} - \frac{27}{8} + \frac{6}{1}$

Multiply $\frac{6}{1}$ by $\frac{8}{8}$ .

$f (- 3) = \frac{- 2 \cdot 8}{8} - \frac{27}{8} + \frac{6}{1} \cdot \frac{8}{8}$

Multiply $\frac{6}{1}$ by $\frac{8}{8}$ .

$f (- 3) = \frac{- 2 \cdot 8}{8} - \frac{27}{8} + \frac{6 \cdot 8}{8}$

Combine the numerators over the common denominator.

$f (- 3) = \frac{- 2 \cdot 8 - 27 + 6 \cdot 8}{8}$

Simplify each term.

Multiply $- 2$ by $8$ .

$f (- 3) = \frac{- 16 - 27 + 6 \cdot 8}{8}$

Multiply $6$ by $8$ .

$f (- 3) = \frac{- 16 - 27 + 48}{8}$

Simplify by adding and subtracting.

Subtract $27$ from $- 16$ .

$f (- 3) = \frac{- 43 + 48}{8}$

Add $- 43$ and $48$ .

$f (- 3) = \frac{5}{8}$

The final answer is $\frac{5}{8}$ .

$\frac{5}{8}$

Convert $\frac{5}{8}$ to decimal.

$y = 0.625$

Step 5

Find the point at $x = - 1$ .

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

$f (- 1) = \frac{{(- 1)}^{3}}{8} + \frac{{(- 1)}^{2}}{2} - \frac{- 1}{2} - 2$

Simplify the result.

Combine fractions.

Combine the numerators over the common denominator.

$f (- 1) = - 2 + \frac{{(- 1)}^{3}}{8} + \frac{{(- 1)}^{2} + 1}{2}$

Simplify the expression.

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

$f (- 1) = - 2 + \frac{{(- 1)}^{3}}{8} + \frac{1 + 1}{2}$

Add $1$ and $1$ .

$f (- 1) = - 2 + \frac{{(- 1)}^{3}}{8} + \frac{2}{2}$

Simplify each term.

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

$f (- 1) = - 2 + \frac{- 1}{8} + \frac{2}{2}$

Move the negative in front of the fraction.

$f (- 1) = - 2 - \frac{1}{8} + \frac{2}{2}$

Divide $2$ by $2$ .

$f (- 1) = - 2 - \frac{1}{8} + 1$

Find the common denominator.

Write $- 2$ as a fraction with denominator $1$ .

$f (- 1) = \frac{- 2}{1} - \frac{1}{8} + 1$

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$f (- 1) = \frac{- 2}{1} \cdot \frac{8}{8} - \frac{1}{8} + 1$

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$f (- 1) = \frac{- 2 \cdot 8}{8} - \frac{1}{8} + 1$

Write $1$ as a fraction with denominator $1$ .

$f (- 1) = \frac{- 2 \cdot 8}{8} - \frac{1}{8} + \frac{1}{1}$

Multiply $\frac{1}{1}$ by $\frac{8}{8}$ .

$f (- 1) = \frac{- 2 \cdot 8}{8} - \frac{1}{8} + \frac{1}{1} \cdot \frac{8}{8}$

Multiply $\frac{1}{1}$ by $\frac{8}{8}$ .

$f (- 1) = \frac{- 2 \cdot 8}{8} - \frac{1}{8} + \frac{8}{8}$

Combine the numerators over the common denominator.

$f (- 1) = \frac{- 2 \cdot 8 - 1 + 8}{8}$

Simplify the expression.

Multiply $- 2$ by $8$ .

$f (- 1) = \frac{- 16 - 1 + 8}{8}$

Subtract $1$ from $- 16$ .

$f (- 1) = \frac{- 17 + 8}{8}$

Add $- 17$ and $8$ .

$f (- 1) = \frac{- 9}{8}$

Move the negative in front of the fraction.

$f (- 1) = - \frac{9}{8}$

The final answer is $- \frac{9}{8}$ .

$- \frac{9}{8}$

Convert $- \frac{9}{8}$ to decimal.

$y = - 1.125$

Step 6

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

$\begin{array}{c} x & y \\ - 3 & 0.625 \\ - 2 & 0 \\ - 1 & - 1.125 \\ 0 & - 2 \\ 2 & 0 \end{array}$

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

$\begin{array}{c} x & y \\ - 3 & 0.625 \\ - 2 & 0 \\ - 1 & - 1.125 \\ 0 & - 2 \\ 2 & 0 \end{array}$

Step 8

Graph f(x)=1/8(x+4)(x+2)(x-2)

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