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

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

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

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

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

Simplify each term.

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

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

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

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{1}{4} + 3 \cdot \frac{4}{4}$

Combine $3$ and $\frac{4}{4}$ .

$y = \frac{1}{4} + \frac{3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$y = \frac{1 + 12}{4}$

Add $1$ and $12$ .

$y = \frac{13}{4}$

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{1 + 6}{2}$

Add $1$ and $6$ .

$y = \frac{7}{2}$

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

$y = 2^{0} + 3$

Simplify $2^{0} + 3$ .

Anything raised to $0$ is $1$ .

$y = 1 + 3$

Add $1$ and $3$ .

$y = 4$

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

$y = 2^{1} + 3$

Simplify $2^{1} + 3$ .

Evaluate the exponent.

$y = 2 + 3$

Add $2$ and $3$ .

$y = 5$

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

$y = 2^{2} + 3$

Simplify $2^{2} + 3$ .

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

$y = 4 + 3$

Add $4$ and $3$ .

$y = 7$

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

$\begin{array}{c} x & y \\ - 2 & \frac{13}{4} \\ - 1 & \frac{7}{2} \\ 0 & 4 \\ 1 & 5 \\ 2 & 7 \end{array}$

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

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