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

$g (x) = 3^{x} - 3$

Step 1

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

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

Step 2

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

Simplify each term.

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

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

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

$y = \frac{1}{9} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{1}{9} - 3 \cdot \frac{9}{9}$

Combine $- 3$ and $\frac{9}{9}$ .

$y = \frac{1}{9} + \frac{- 3 \cdot 9}{9}$

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 9}{9}$

Simplify the numerator.

Multiply $- 3$ by $9$ .

$y = \frac{1 - 27}{9}$

Subtract $27$ from $1$ .

$y = \frac{- 26}{9}$

Move the negative in front of the fraction.

$y = - \frac{26}{9}$

Step 3

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

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

Step 4

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $3$ .

$y = \frac{1 - 9}{3}$

Subtract $9$ from $1$ .

$y = \frac{- 8}{3}$

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

Step 5

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

$y = 3^{0} - 3$

Step 6

Simplify $3^{0} - 3$ .

Anything raised to $0$ is $1$ .

$y = 1 - 3$

Subtract $3$ from $1$ .

$y = - 2$

Step 7

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

$y = 3^{1} - 3$

Step 8

Simplify $3^{1} - 3$ .

Evaluate the exponent.

$y = 3 - 3$

Subtract $3$ from $3$ .

$y = 0$

Step 9

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

$y = 3^{2} - 3$

Step 10

Simplify $3^{2} - 3$ .

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

$y = 9 - 3$

Subtract $3$ from $9$ .

$y = 6$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{26}{9} \\ - 1 & - \frac{8}{3} \\ 0 & - 2 \\ 1 & 0 \\ 2 & 6 \end{array}$

Step 12

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

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