Calculus Examples

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

Step 1

Set the denominator in $\frac{x}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

The domain is all values of $x$ that make the expression defined.

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 0}$

Step 3

$y = 1$ is a straight line perpendicular to the $y$ -axis, which means that the range is a set of one value ${y | y = 1}$ .

Set-Builder Notation:

${y | y = 1}$

Step 4

Determine the domain and range.

Domain: $(- \infty, 0) \cup (0, \infty), {x | x \neq 0}$

Range: ${y | y = 1}$

Step 5