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

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

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

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

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

Multiply $2$ by $- 2$ .

$y = e^{- 4}$

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

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

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

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

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

Multiply $2$ by $- 1$ .

$y = e^{- 2}$

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

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

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

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

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

Multiply $2$ by $0$ .

$y = e^{0}$

Anything raised to $0$ is $1$ .

$y = 1$

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

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

Multiply $2$ by $1$ .

$y = e^{2}$

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

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

Multiply $2$ by $2$ .

$y = e^{4}$

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

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