Graph Using a Table of Values f(x)=4^(-x)

$f (x) = 4^{- x}$

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

$y = 4^{- (- 2)}$

Simplify $4^{- (- 2)}$ .

Multiply $- 1$ by $- 2$ .

$y = 4^{2}$

Raise $4$ to the power of $2$ .

$y = 16$

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

$y = 4^{- (- 1)}$

Simplify $4^{- (- 1)}$ .

Multiply $- 1$ by $- 1$ .

$y = 4^{1}$

Evaluate the exponent.

$y = 4$

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

$y = 4^{- (0)}$

Simplify $4^{- (0)}$ .

Multiply $- 1$ by $0$ .

$y = 4^{0}$

Anything raised to $0$ is $1$ .

$y = 1$

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

$y = 4^{- (1)}$

Simplify $4^{- (1)}$ .

Multiply $- 1$ by $1$ .

$y = 4^{- 1}$

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

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

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

$y = 4^{- (2)}$

Simplify $4^{- (2)}$ .

Multiply $- 1$ by $2$ .

$y = 4^{- 2}$

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

$y = \frac{1}{4^{2}}$

Raise $4$ to the power of $2$ .

$y = \frac{1}{16}$

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

$\begin{array}{c} x & y \\ - 2 & 16 \\ - 1 & 4 \\ 0 & 1 \\ 1 & \frac{1}{4} \\ 2 & \frac{1}{16} \end{array}$