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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

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

$y = 3^{2} - 2$

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

$y = 9 - 2$

Subtract $2$ from $9$ .

$y = 7$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

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

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

$y = 3 - 2$

Subtract $2$ from $3$ .

$y = 1$

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

Apply the product rule to $\frac{1}{3}$ .

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

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Divide $1$ by $1$ .

$y = 1 - 2$

Subtract $2$ from $1$ .

$y = - 1$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

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

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $3$ .

$y = \frac{1 - 6}{3}$

Subtract $6$ from $1$ .

$y = \frac{- 5}{3}$

Move the negative in front of the fraction.

$y = - \frac{5}{3}$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

Apply the product rule to $\frac{1}{3}$ .

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

One to any power is one.

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

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

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

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $9$ .

$y = \frac{1 - 18}{9}$

Subtract $18$ from $1$ .

$y = \frac{- 17}{9}$

Move the negative in front of the fraction.

$y = - \frac{17}{9}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 7 \\ - 1 & 1 \\ 0 & - 1 \\ 1 & - \frac{5}{3} \\ 2 & - \frac{17}{9} \end{array}$

Step 12

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

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