Question

1. what is the domain of the rational function $f(x)=\frac{x+4}{(x-3)(x+5)}$ shown in the graph below?

$\\{x | x \
eq 3 \text{ and } x \
eq 5\\}$
$\\{x | x \
eq -4, x \
eq -5, \text{ and } x \
eq 3\\}$

Explanation:

Step1: Identify denominator zeros

Set $(x-3)(x+5)=0$. Solve for $x$:
$x-3=0 \implies x=3$; $x+5=0 \implies x=-5$

Step2: Define domain of rational function

Rational functions are undefined where denominator is 0. So exclude $x=3$ and $x=-5$ from all real numbers.

Answer:

$\{x \mid x
eq 3 \text{ and } x
eq -5\}$