Find the Domain and Range (x+6)/(x-7)

$\frac{x + 6}{x - 7}$

Step 1

Set the denominator in $\frac{x + 6}{x - 7}$ equal to $0$ to find where the expression is undefined.

$x - 7 = 0$

Step 2

Add $7$ to both sides of the equation.

$x = 7$

Step 3

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

Interval Notation:

$(- \infty, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \neq 7}$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

${y | y \neq 1}$

Step 5

Determine the domain and range.

Domain: $(- \infty, 7) \cup (7, \infty), {x | x \neq 7}$

Range: $(- \infty, 1) \cup (1, \infty), {y | y \neq 1}$

Step 6