Find the Domain and Range y=1/(x-3)+6

$y = \frac{1}{x - 3} + 6$

Step 1

Set the denominator in $\frac{1}{x - 3}$ equal to $0$ to find where the expression is undefined.

$x - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$x = 3$

Step 3

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

Interval Notation:

$(- \infty, 3) \cup (3, \infty)$

Set-Builder Notation:

${x | x \neq 3}$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

${y | y \neq 6}$

Step 5

Determine the domain and range.

Domain: $(- \infty, 3) \cup (3, \infty), {x | x \neq 3}$

Range: $(- \infty, 6) \cup (6, \infty), {y | y \neq 6}$

Step 6