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

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

Step 1

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

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

Step 2

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

Simplify each term.

Subtract $3$ from $- 2$ .

$y = 3^{- 5} + 2$

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

$y = \frac{1}{3^{5}} + 2$

Raise $3$ to the power of $5$ .

$y = \frac{1}{243} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{243}{243}$ .

$y = \frac{1}{243} + 2 \cdot \frac{243}{243}$

Combine $2$ and $\frac{243}{243}$ .

$y = \frac{1}{243} + \frac{2 \cdot 243}{243}$

Combine the numerators over the common denominator.

$y = \frac{1 + 2 \cdot 243}{243}$

Simplify the numerator.

Multiply $2$ by $243$ .

$y = \frac{1 + 486}{243}$

Add $1$ and $486$ .

$y = \frac{487}{243}$

Step 3

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

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

Step 4

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

Simplify each term.

Subtract $3$ from $- 1$ .

$y = 3^{- 4} + 2$

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

$y = \frac{1}{3^{4}} + 2$

Raise $3$ to the power of $4$ .

$y = \frac{1}{81} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{81}{81}$ .

$y = \frac{1}{81} + 2 \cdot \frac{81}{81}$

Combine $2$ and $\frac{81}{81}$ .

$y = \frac{1}{81} + \frac{2 \cdot 81}{81}$

Combine the numerators over the common denominator.

$y = \frac{1 + 2 \cdot 81}{81}$

Simplify the numerator.

Multiply $2$ by $81$ .

$y = \frac{1 + 162}{81}$

Add $1$ and $162$ .

$y = \frac{163}{81}$

Step 5

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

$y = 3^{(0) - 3} + 2$

Step 6

Simplify $3^{(0) - 3} + 2$ .

Simplify each term.

Subtract $3$ from $0$ .

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

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

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

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

$y = \frac{1}{27} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$y = \frac{1}{27} + 2 \cdot \frac{27}{27}$

Combine $2$ and $\frac{27}{27}$ .

$y = \frac{1}{27} + \frac{2 \cdot 27}{27}$

Combine the numerators over the common denominator.

$y = \frac{1 + 2 \cdot 27}{27}$

Simplify the numerator.

Multiply $2$ by $27$ .

$y = \frac{1 + 54}{27}$

Add $1$ and $54$ .

$y = \frac{55}{27}$

Step 7

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

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

Step 8

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

Simplify each term.

Subtract $3$ from $1$ .

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

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

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

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 $9$ .

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

Add $1$ and $18$ .

$y = \frac{19}{9}$

Step 9

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

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

Step 10

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

Simplify each term.

Subtract $3$ from $2$ .

$y = 3^{- 1} + 2$

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

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

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 $3$ .

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

Add $1$ and $6$ .

$y = \frac{7}{3}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{487}{243} \\ - 1 & \frac{163}{81} \\ 0 & \frac{55}{27} \\ 1 & \frac{19}{9} \\ 2 & \frac{7}{3} \end{array}$

Step 12

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

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