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

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

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

Step 2.2

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

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

Step 3

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

$y = 2^{- 1}$

Step 4

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

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

Step 5

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

$y = 2^{0}$

Step 6

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

Evaluate the exponent.

$y = 2$

Step 9

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

$y = 2^{2}$

Step 10

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

$y = 4$

Step 11

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

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

Step 12