Graph Using a Table of Values y=3^(-x)

$y = 3^{- x}$

Step 1

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

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

Step 2

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

Multiply $- 1$ by $- 2$ .

$y = 3^{2}$

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

$y = 9$

Step 3

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

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

Step 4

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

Multiply $- 1$ by $- 1$ .

$y = 3^{1}$

Evaluate the exponent.

$y = 3$

Step 5

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

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

Step 6

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

Multiply $- 1$ by $0$ .

$y = 3^{0}$

Anything raised to $0$ is $1$ .

$y = 1$

Step 7

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

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

Step 8

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

Multiply $- 1$ by $1$ .

$y = 3^{- 1}$

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

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

Step 9

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

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

Step 10

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

Multiply $- 1$ by $2$ .

$y = 3^{- 2}$

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

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

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

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

Step 11

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

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

Step 12

Graph Using a Table of Values y=3^(-x)

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