Graph Using a Table of Values f(x)=(1/9)^x

$f (x) = {(\frac{1}{9})}^{x}$

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

$y = {(\frac{1}{9})}^{- 2}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{9})}^{- 2}$

Simplify ${(\frac{1}{9})}^{- 2}$ .

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 9^{2}$

Raise $9$ to the power of $2$ .

$y = 81$

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

$y = {(\frac{1}{9})}^{- 1}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{9})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 9$

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

$y = {(\frac{1}{9})}^{0}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{9})}^{0}$

Simplify ${(\frac{1}{9})}^{0}$ .

Apply the product rule to $\frac{1}{9}$ .

$y = \frac{1^{0}}{9^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{9^{0}}$

Anything raised to $0$ is $1$ .

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

Divide $1$ by $1$ .

$y = 1$

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

$y = {(\frac{1}{9})}^{1}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

$y = {(\frac{1}{9})}^{2}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{9})}^{2}$

Simplify ${(\frac{1}{9})}^{2}$ .

Apply the product rule to $\frac{1}{9}$ .

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

One to any power is one.

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

Raise $9$ to the power of $2$ .

$y = \frac{1}{81}$

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

$\begin{array}{c} x & y \\ - 2 & 81 \\ - 1 & 9 \\ 0 & 1 \\ 1 & \frac{1}{9} \\ 2 & \frac{1}{81} \end{array}$

Graph Using a Table of Values f(x)=(1/9)^x

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