Graph the ralional function. \[ \text { (i) } \frac{4 x}{x^{2}-36} \] (A) (B) (c)

Step 1 ：First, we need to find the domain of the function. The function is defined when the denominator is not equal to 0, i.e., we must have $x^2-36\neq0$. Factoring, we get $(x-6)(x+6)\neq0$. So the domain of the function is $x\neq-6 \text{ and } x\neq6$, or $x \in \boxed{(-\infty, -6) \cup (-6, 6) \cup (6, \infty)}$ in interval notation.

Step 2 ：Next, we find the vertical asymptotes. Vertical asymptotes occur when the denominator is equal to 0. From the domain, we know that the vertical asymptotes are at $x=-6$ and $x=6$.

Step 3 ：Then, we find the horizontal asymptote. The horizontal asymptote occurs when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 1 and the degree of the denominator is 2. So, the horizontal asymptote is at $y=0$.

Step 4 ：Finally, we can graph the function. Plot the vertical asymptotes at $x=-6$ and $x=6$, and the horizontal asymptote at $y=0$. Then, sketch the graph of the function, making sure it approaches the asymptotes as $x$ approaches $-6$, $6$, and $\pm\infty$.