Algebra Examples

$f (x) = \frac{1}{2 x}$

Step 1

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

$y = \frac{1}{2 (- 2)}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = \frac{1}{2 (- 2)}$

Step 2.2

Simplify $\frac{1}{2 (- 2)}$ .

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Step 2.2.1

Multiply $2$ by $- 2$ .

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

Step 2.2.2

Move the negative in front of the fraction.

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

Step 3

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

$y = \frac{1}{2 (- 1)}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = \frac{1}{2 (- 1)}$

Step 4.2

Cancel the common factor of $1$ and $- 1$ .

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Step 4.2.1

Rewrite $1$ as $- 1 (- 1)$ .

$y = \frac{- 1 (- 1)}{2 (- 1)}$

Step 4.2.2

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

Cancel the common factor of $1$ .

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Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Rewrite the expression.

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Multiply $2$ by $2$ .

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

Step 9

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

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

Step 10