Graph Using a Table of Values y=2^x-1

$y = 2^{x} - 1$

Step 1

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

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

Step 2

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

Simplify each term.

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

$y = \frac{1}{2^{2}} - 1$

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

$y = \frac{1}{4} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{1}{4} - 1 \cdot \frac{4}{4}$

Combine $- 1$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

$y = \frac{1 - 1 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 1$ by $4$ .

$y = \frac{1 - 4}{4}$

Subtract $4$ from $1$ .

$y = \frac{- 3}{4}$

Move the negative in front of the fraction.

$y = - \frac{3}{4}$

Step 3

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

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

Step 4

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

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

$y = \frac{1}{2} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{1}{2} - 1 \cdot \frac{2}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

$y = \frac{1 - 1 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$y = \frac{1 - 2}{2}$

Subtract $2$ from $1$ .

$y = \frac{- 1}{2}$

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 5

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

$y = 2^{0} - 1$

Step 6

Simplify $2^{0} - 1$ .

Anything raised to $0$ is $1$ .

$y = 1 - 1$

Subtract $1$ from $1$ .

$y = 0$

Step 7

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

$y = 2^{1} - 1$

Step 8

Simplify $2^{1} - 1$ .

Evaluate the exponent.

$y = 2 - 1$

Subtract $1$ from $2$ .

$y = 1$

Step 9

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

$y = 2^{2} - 1$

Step 10

Simplify $2^{2} - 1$ .

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

$y = 4 - 1$

Subtract $1$ from $4$ .

$y = 3$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{3}{4} \\ - 1 & - \frac{1}{2} \\ 0 & 0 \\ 1 & 1 \\ 2 & 3 \end{array}$

Step 12

Graph Using a Table of Values y=2^x-1

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