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

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq - 4}$

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

Interval Notation:

$(- \infty, - 6 - 4 \sqrt{3}] \cup [- 6 + 4 \sqrt{3}, \infty)$

Set-Builder Notation:

${y | y \leq - 6 - 4 \sqrt{3}, y \geq - 6 + 4 \sqrt{3}}$

Determine the domain and range.

Domain: $(- \infty, - 4) \cup (- 4, \infty), {x | x \neq - 4}$

Range: $(- \infty, - 6 - 4 \sqrt{3}] \cup [- 6 + 4 \sqrt{3}, \infty), {y | y \leq - 6 - 4 \sqrt{3}, y \geq - 6 + 4 \sqrt{3}}$