Graph Using a Table of Values f(x)=4/3(2)^x

$f (x) = \frac{4}{3} {(2)}^{x}$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

Combine.

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

Simplify the expression.

Multiply $4$ by $1$ .

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

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

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

Multiply $3$ by $4$ .

$y = \frac{4}{12}$

Cancel the common factor of $4$ and $12$ .

Factor $4$ out of $4$ .

$y = \frac{4 (1)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{1}{3}$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Simplify $\frac{4}{3} \cdot {(2)}^{- 1}$ .

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{2 (2)}{3} \cdot \frac{1}{2}$

Cancel the common factor.

$y = \frac{2 \cdot 2}{3} \cdot \frac{1}{2}$

Rewrite the expression.

$y = \frac{2}{3}$

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

$y = \frac{4}{3} \cdot {(2)}^{0}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{4}{3} \cdot 2^{0}$

Remove parentheses.

$y = \frac{4}{3} \cdot {(2)}^{0}$

Simplify $\frac{4}{3} \cdot {(2)}^{0}$ .

Anything raised to $0$ is $1$ .

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

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

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

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Multiply $\frac{4}{3} (2)$ .

Combine $\frac{4}{3}$ and $2$ .

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

Multiply $4$ by $2$ .

$y = \frac{8}{3}$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

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

Combine $\frac{4}{3}$ and $4$ .

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

Multiply $4$ by $4$ .

$y = \frac{16}{3}$

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

$\begin{array}{c} x & y \\ - 2 & \frac{1}{3} \\ - 1 & \frac{2}{3} \\ 0 & \frac{4}{3} \\ 1 & \frac{8}{3} \\ 2 & \frac{16}{3} \end{array}$

Graph Using a Table of Values f(x)=4/3(2)^x

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