Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Multiply $- 1$ by $- 2$ .

$y = 2^{2}$

Step 2.2

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

$y = 4$

Step 3

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

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

Step 4

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

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Step 4.1

Multiply $- 1$ by $- 1$ .

$y = 2^{1}$

Step 4.2

Evaluate the exponent.

$y = 2$

Step 5

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

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

Step 6

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

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Step 6.1

Multiply $- 1$ by $0$ .

$y = 2^{0}$

Step 6.2

Anything raised to $0$ is $1$ .

$y = 1$

Step 7

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

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

Step 8

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

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Step 8.1

Multiply $- 1$ by $1$ .

$y = 2^{- 1}$

Step 8.2

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

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

Step 9

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

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

Step 10

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

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Step 10.1

Multiply $- 1$ by $2$ .

$y = 2^{- 2}$

Step 10.2

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

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

Step 10.3

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

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

Step 11

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

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

Step 12