Question

using interval notation, state the domain of the rational function. $y = \frac{x - 3}{x + 4}$
$(-\infty, - 4)\cup(-4, \infty)$
$(-\infty, - 3)\cup(-3, \infty)$
$(-\infty, 4)\cup(4, \infty)$
$(-\infty, 3)\cup(3, \infty)$

Explanation:

Step1: Recall domain rule for rational functions

The denominator of a rational function cannot be zero. For $y = \frac{x - 3}{x + 4}$, we set $x+4
eq0$.

Step2: Solve for x

Solving $x + 4
eq0$ gives $x
eq - 4$.

Step3: Write in interval notation

The domain is all real - numbers except $x=-4$, which is written as $(-\infty,-4)\cup(-4,\infty)$.

Answer:

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