Find the Domain and Range r(x)=(x^2-4x-5)/(x+1)

$r (x) = \frac{x^{2} - 4 x - 5}{x + 1}$

Step 1

Set the denominator in $\frac{x^{2} - 4 x - 5}{x + 1}$ equal to $0$ to find where the expression is undefined.

$x + 1 = 0$

Step 2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

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

Interval Notation:

$(- \infty, - 1) \cup (- 1, \infty)$

Set-Builder Notation:

${x | x \neq - 1}$

Step 4

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

Interval Notation:

$(- \infty, - 6) \cup (- 6, \infty)$

Set-Builder Notation:

${y | y \neq - 6}$

Step 5

Determine the domain and range.

Domain: $(- \infty, - 1) \cup (- 1, \infty), {x | x \neq - 1}$

Range: $(- \infty, - 6) \cup (- 6, \infty), {y | y \neq - 6}$

Step 6