Algebra Examples

$y = e^{- 2 x}$

Step 1

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

$y = e^{- 2 \cdot - 2}$

Step 2

Multiply $- 2$ by $- 2$ .

$y = e^{4}$

Step 3

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

$y = e^{- 2 \cdot - 1}$

Step 4

Multiply $- 2$ by $- 1$ .

$y = e^{2}$

Step 5

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

$y = e^{- 2 \cdot 0}$

Step 6

Simplify $e^{- 2 \cdot 0}$ .

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Step 6.1

Multiply $- 2$ by $0$ .

$y = e^{0}$

Step 6.2

Anything raised to $0$ is $1$ .

$y = 1$

Step 7

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

$y = e^{- 2 \cdot 1}$

Step 8

Simplify $e^{- 2 \cdot 1}$ .

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Step 8.1

Multiply $- 2$ by $1$ .

$y = e^{- 2}$

Step 8.2

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

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

Step 9

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

$y = e^{- 2 \cdot 2}$

Step 10

Simplify $e^{- 2 \cdot 2}$ .

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Step 10.1

Multiply $- 2$ by $2$ .

$y = e^{- 4}$

Step 10.2

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

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

Step 11

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

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

Step 12