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

$f (x) = 3^{x} + 2$

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

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

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

Simplify each term.

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 $18$ .

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

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

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

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

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 $6$ .

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

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

$y = 3^{0} + 2$

Simplify $3^{0} + 2$ .

Anything raised to $0$ is $1$ .

$y = 1 + 2$

Add $1$ and $2$ .

$y = 3$

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

$y = 3^{1} + 2$

Simplify $3^{1} + 2$ .

Evaluate the exponent.

$y = 3 + 2$

Add $3$ and $2$ .

$y = 5$

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

$y = 3^{2} + 2$

Simplify $3^{2} + 2$ .

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

$y = 9 + 2$

Add $9$ and $2$ .

$y = 11$

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

$\begin{array}{c} x & y \\ - 2 & \frac{19}{9} \\ - 1 & \frac{7}{3} \\ 0 & 3 \\ 1 & 5 \\ 2 & 11 \end{array}$

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

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