Graph Using a Table of Values f(x)=2^(x+1)+3

$f (x) = 2^{x + 1} + 3$

Step 1

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

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

Step 2

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

Simplify each term.

Add $- 2$ and $1$ .

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

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 $6$ .

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

Step 3

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

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

Step 4

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

Simplify each term.

Add $- 1$ and $1$ .

$y = 2^{0} + 3$

Anything raised to $0$ is $1$ .

$y = 1 + 3$

Add $1$ and $3$ .

$y = 4$

Step 5

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

$y = 2^{(0) + 1} + 3$

Step 6

Simplify $2^{(0) + 1} + 3$ .

Simplify each term.

Add $0$ and $1$ .

$y = 2^{1} + 3$

Evaluate the exponent.

$y = 2 + 3$

Add $2$ and $3$ .

$y = 5$

Step 7

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

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

Step 8

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

Simplify each term.

Add $1$ and $1$ .

$y = 2^{2} + 3$

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

$y = 4 + 3$

Add $4$ and $3$ .

$y = 7$

Step 9

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

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

Step 10

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

Simplify each term.

Add $2$ and $1$ .

$y = 2^{3} + 3$

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

$y = 8 + 3$

Add $8$ and $3$ .

$y = 11$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{7}{2} \\ - 1 & 4 \\ 0 & 5 \\ 1 & 7 \\ 2 & 11 \end{array}$

Step 12

Graph Using a Table of Values f(x)=2^(x+1)+3

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