Graph Using a Table of Values f(x)=-4/3(3)^x

$f (x) = - \frac{4}{3} {(3)}^{x}$

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = - \frac{4}{3} \cdot {(3)}^{- 2}$

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{4}{3} \cdot 3^{- 2}$

Remove parentheses.

$y = - \frac{4}{3} \cdot {(3)}^{- 2}$

Simplify $- \frac{4}{3} \cdot {(3)}^{- 2}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = - \frac{4}{3} \cdot \frac{1}{3^{2}}$

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

$y = - \frac{4}{3} \cdot \frac{1}{9}$

Multiply $- \frac{4}{3} \cdot \frac{1}{9}$ .

Multiply $\frac{1}{9}$ by $\frac{4}{3}$ .

$y = - \frac{4}{9 \cdot 3}$

Multiply $9$ by $3$ .

$y = - \frac{4}{27}$

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = - \frac{4}{3} \cdot {(3)}^{- 1}$

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{4}{3} \cdot 3^{- 1}$

Remove parentheses.

$y = - \frac{4}{3} \cdot {(3)}^{- 1}$

Simplify $- \frac{4}{3} \cdot {(3)}^{- 1}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = - \frac{4}{3} \cdot \frac{1}{3}$

Multiply $- \frac{4}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{3}$ by $\frac{4}{3}$ .

$y = - \frac{4}{3 \cdot 3}$

Multiply $3$ by $3$ .

$y = - \frac{4}{9}$

Substitute $0$ for $x$ and find the result for $y$ .

$y = - \frac{4}{3} \cdot {(3)}^{0}$

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{4}{3} \cdot 3^{0}$

Remove parentheses.

$y = - \frac{4}{3} \cdot {(3)}^{0}$

Simplify $- \frac{4}{3} \cdot {(3)}^{0}$ .

Anything raised to $0$ is $1$ .

$y = - \frac{4}{3} \cdot 1$

Multiply $- 1$ by $1$ .

$y = - \frac{4}{3}$

Substitute $1$ for $x$ and find the result for $y$ .

$y = - \frac{4}{3} \cdot {(3)}^{1}$

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{4}{3} \cdot 3$

Remove parentheses.

$y = - \frac{4}{3} \cdot 3$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$y = \frac{- 4}{3} \cdot 3$

Cancel the common factor.

$y = \frac{- 4}{3} \cdot 3$

Rewrite the expression.

$y = - 4$

Substitute $2$ for $x$ and find the result for $y$ .

$y = - \frac{4}{3} \cdot {(3)}^{2}$

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{4}{3} \cdot 3^{2}$

Remove parentheses.

$y = - \frac{4}{3} \cdot {(3)}^{2}$

Simplify $- \frac{4}{3} \cdot {(3)}^{2}$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$y = \frac{- 4}{3} \cdot {(3)}^{2}$

Factor $3$ out of ${(3)}^{2}$ .

$y = \frac{- 4}{3} \cdot (3 \cdot 3)$

Cancel the common factor.

$y = \frac{- 4}{3} \cdot (3 \cdot 3)$

Rewrite the expression.

$y = - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$y = - 12$

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \frac{4}{27} \\ - 1 & - \frac{4}{9} \\ 0 & - \frac{4}{3} \\ 1 & - 4 \\ 2 & - 12 \end{array}$

Graph Using a Table of Values f(x)=-4/3(3)^x

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