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

$f (x) = \frac{2 (x + 5)}{(x - 3)}$

Set the denominator in $\frac{2 (x + 5)}{x - 3}$ equal to $0$ to find where the expression is undefined.

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 3}$

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

Interval Notation:

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

Set-Builder Notation:

${y | y \neq 2}$

Determine the domain and range.

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

Range: $(- \infty, 2) \cup (2, \infty), {y | y \neq 2}$