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

$f (x) = 2^{- x}$

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

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

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

Multiply $- 1$ by $- 2$ .

$y = 2^{2}$

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

$y = 4$

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

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

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

Multiply $- 1$ by $- 1$ .

$y = 2^{1}$

Evaluate the exponent.

$y = 2$

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

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

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

Multiply $- 1$ by $0$ .

$y = 2^{0}$

Anything raised to $0$ is $1$ .

$y = 1$

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

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

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

Multiply $- 1$ by $1$ .

$y = 2^{- 1}$

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

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

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

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

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

Multiply $- 1$ by $2$ .

$y = 2^{- 2}$

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

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

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

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

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

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