Algebra Examples

f (x) = 2^{x}

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

Step 1

Substitute

- 2

$- 2$ for

x

$x$ and find the result for

y

$y$ .

y = 2^{- 2}

$y = 2^{- 2}$

Step 2

Simplify

2^{- 2}

$2^{- 2}$ .

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Step 2.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 2.2

Raise

2

$2$ to the power of

2

$2$ .

y = \frac{1}{4}

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

y = \frac{1}{4}

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

Step 3

Substitute

- 1

$- 1$ for

x

$x$ and find the result for

y

$y$ .

y = 2^{- 1}

$y = 2^{- 1}$

Step 4

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

y = \frac{1}{2}

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

Step 5

Substitute

0

$0$ for

x

$x$ and find the result for

y

$y$ .

y = 2^{0}

$y = 2^{0}$

Step 6

Anything raised to

0

$0$ is

1

$1$ .

y = 1

$y = 1$

Step 7

Substitute

1

$1$ for

x

$x$ and find the result for

y

$y$ .

y = 2^{1}

$y = 2^{1}$

Step 8

Evaluate the exponent.

y = 2

$y = 2$

Step 9

Substitute

2

$2$ for

x

$x$ and find the result for

y

$y$ .

y = 2^{2}

$y = 2^{2}$

Step 10

Raise

2

$2$ to the power of

2

$2$ .

y = 4

$y = 4$

Step 11

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

\begin{matrix} x & y - 2 & \frac{1}{4} - 1 & \frac{1}{2} 0 & 1 1 & 2 2 & 4 \end{matrix}

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

Step 12