Find the Domain and Range 2/(x-3)-5

$\frac{2}{x - 3} - 5$

Step 1

Set the denominator in $\frac{2}{x - 3}$ 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:

$(- \infty, - 5) \cup (- 5, \infty)$

Set-Builder Notation:

${y | y \neq - 5}$

Step 5

Determine the domain and range.

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

Range: $(- \infty, - 5) \cup (- 5, \infty), {y | y \neq - 5}$

Step 6