Graph Using a Table of Values y=1/2(3)^x

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

Combine.

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

Simplify the expression.

Multiply $1$ by $1$ .

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

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

$y = \frac{1}{2 \cdot 9}$

Multiply $2$ by $9$ .

$y = \frac{1}{18}$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

Multiply $\frac{1}{2} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{3}$ .

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

Multiply $2$ by $3$ .

$y = \frac{1}{6}$

Step 5

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

$y = \frac{1}{2} \cdot {(3)}^{0}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{1}{2} \cdot 3^{0}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(3)}^{0}$

Simplify $\frac{1}{2} \cdot {(3)}^{0}$ .

Anything raised to $0$ is $1$ .

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

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

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

$y = \frac{1}{2} \cdot 9$

Combine $\frac{1}{2}$ and $9$ .

$y = \frac{9}{2}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{1}{18} \\ - 1 & \frac{1}{6} \\ 0 & \frac{1}{2} \\ 1 & \frac{3}{2} \\ 2 & \frac{9}{2} \end{array}$

Step 12

Graph Using a Table of Values y=1/2(3)^x

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