Find the Domain and Range f(x)=(x^2-4)/(x-2)

$f (x) = \frac{x^{2} - 4}{x - 2}$

Set the denominator in $\frac{x^{2} - 4}{x - 2}$ equal to $0$ to find where the expression is undefined.

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 2}$

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

Interval Notation:

$(- \infty, 4) \cup (4, \infty)$

Set-Builder Notation:

${y | y \neq 4}$

Determine the domain and range.

Domain: $(- \infty, 2) \cup (2, \infty), {x | x \neq 2}$

Range: $(- \infty, 4) \cup (4, \infty), {y | y \neq 4}$