Question

determine the domain and the equations of the asymptotes for the graph of the r
the domain is (-∞,3)∪(3,∞). (simplify your answer. type your answer in interval notation.)
the asymptotes are x = 3 and y = . (simplify your answers.)

Explanation:

Step1: Recall domain concept

The domain of a rational - function is all real numbers except the values that make the denominator zero. Since the domain is given as $(-\infty,3)\cup(3,\infty)$, the function is undefined at $x = 3$.

Step2: Analyze vertical asymptote

A vertical asymptote occurs at the value of $x$ that makes the denominator of a rational function zero. Here, the vertical asymptote is $x = 3$.

Step3: Determine horizontal asymptote

For a rational function $\frac{f(x)}{g(x)}$, if the degree of $f(x)$ is less than the degree of $g(x)$, the horizontal asymptote is $y = 0$. Without knowing the function explicitly, but given the domain and one - sided information, assume a simple rational function case where the degree of the numerator is less than the degree of the denominator. So the horizontal asymptote is $y=0$.

Answer:

The domain is $(-\infty,3)\cup(3,\infty)$. The asymptotes are $x = 3$ and $y = 0$.