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Examples

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

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

Step 1

Set the denominator in

\frac{1}{x - 2}

$\frac{1}{x - 2}$ equal to

0

$0$ to find where the expression is undefined.

x - 2 = 0

$x - 2 = 0$

Step 2

Add

2

$2$ to both sides of the equation.

x = 2

$x = 2$

Step 3

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

(- \infty, 2) \cup (2, \infty)

$(- \infty, 2) \cup (2, \infty)$

Set-Builder Notation:

{x | x \neq 2}

${x | x \neq 2}$

Step 4

The range is the set of all valid

y

$y$ values. Use the graph to find the range.

Interval Notation:

(- \infty, 0) \cup (0, \infty)

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

{y | y \neq 0}

${y | y \neq 0}$

Step 5

Determine the domain and range.

Domain:

(- \infty, 2) \cup (2, \infty), {x | x \neq 2}

$(- \infty, 2) \cup (2, \infty), {x | x \neq 2}$

Range:

(- \infty, 0) \cup (0, \infty), {y | y \neq 0}

$(- \infty, 0) \cup (0, \infty), {y | y \neq 0}$

Step 6

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$