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

$y = \frac{x^{2} - 4}{x + 2}$

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

$x + 2 = 0$

Subtract $2$ from 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: $(- \infty, - 4) \cup (- 4, \infty), {y | y \neq - 4}$