Calculus Examples

$f (x) = \frac{5}{x - 6}$

Step 1

Set the denominator in $\frac{5}{x - 6}$ equal to $0$ to find where the expression is undefined.

$x - 6 = 0$

Step 2

Add $6$ to both sides of the equation.

$x = 6$

Step 3

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

Interval Notation:

$(- \infty, 6) \cup (6, \infty)$

Set-Builder Notation:

${x | x \neq 6}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

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

Set-Builder Notation:

${y | y \neq 0}$

Step 5

Determine the domain and range.

Domain: $(- \infty, 6) \cup (6, \infty), {x | x \neq 6}$

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

Step 6