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

$y = 3^{x - 1}$

Step 1

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

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

Step 2

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

Subtract $1$ from $- 2$ .

$y = 3^{- 3}$

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

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

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

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

Step 3

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

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

Step 4

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

Subtract $1$ from $- 1$ .

$y = 3^{- 2}$

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 5

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

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

Step 6

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

Subtract $1$ from $0$ .

$y = 3^{- 1}$

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

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

Step 7

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

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

Step 8

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

Subtract $1$ from $1$ .

$y = 3^{0}$

Anything raised to $0$ is $1$ .

$y = 1$

Step 9

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

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

Step 10

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

Subtract $1$ from $2$ .

$y = 3^{1}$

Evaluate the exponent.

$y = 3$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{1}{27} \\ - 1 & \frac{1}{9} \\ 0 & \frac{1}{3} \\ 1 & 1 \\ 2 & 3 \end{array}$

Step 12

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

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