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

$f (x) = 3 {(2)}^{x}$

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

$y = 3 {(2)}^{- 2}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 3 {(2)}^{- 2}$

Simplify $3 {(2)}^{- 2}$ .

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

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

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

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

Combine $3$ and $\frac{1}{4}$ .

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

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

$y = 3 {(2)}^{- 1}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 3 {(2)}^{- 1}$

Simplify $3 {(2)}^{- 1}$ .

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

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

Combine $3$ and $\frac{1}{2}$ .

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

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

$y = 3 {(2)}^{0}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 3 {(2)}^{0}$

Simplify $3 {(2)}^{0}$ .

Anything raised to $0$ is $1$ .

$y = 3 \cdot 1$

Multiply $3$ by $1$ .

$y = 3$

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

$y = 3 {(2)}^{1}$

Solve the equation for $y$ .

Remove parentheses.

$y = 3 \cdot 2$

Remove parentheses.

$y = 3 (2)$

Multiply $3$ by $2$ .

$y = 6$

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

$y = 3 {(2)}^{2}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 3 {(2)}^{2}$

Simplify $3 {(2)}^{2}$ .

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

$y = 3 \cdot 4$

Multiply $3$ by $4$ .

$y = 12$

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

$\begin{array}{c} x & y \\ - 2 & \frac{3}{4} \\ - 1 & \frac{3}{2} \\ 0 & 3 \\ 1 & 6 \\ 2 & 12 \end{array}$

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

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