Find the Domain and Range (8x)/(x+3)

$\frac{8 x}{x + 3}$

Step 1

Set the denominator in $\frac{8 x}{x + 3}$ equal to $0$ to find where the expression is undefined.

$x + 3 = 0$

Step 2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 3

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

Interval Notation:

$(- \infty, - 3) \cup (- 3, \infty)$

Set-Builder Notation:

${x | x \neq - 3}$

Step 4

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

Interval Notation:

$(- \infty, 8) \cup (8, \infty)$

Set-Builder Notation:

${y | y \neq 8}$

Step 5

Determine the domain and range.

Domain: $(- \infty, - 3) \cup (- 3, \infty), {x | x \neq - 3}$

Range: $(- \infty, 8) \cup (8, \infty), {y | y \neq 8}$

Step 6