list all the asymptotes of the following function, then graph the function. r(x)=7/(x^2 - 36) what is/are…

list all the asymptotes of the following function, then graph the function. r(x)=7/(x^2 - 36) what is/are the equation(s) of the vertical asymptote(s) of r(x)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the vertical asymptote(s) is/are x = - 6,x = 6. (use a comma to separate answers as needed. type an equation(s).) b. there is no vertical asymptote. what is the equation of the oblique asymptote of r(x)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the oblique asymptote is. (type an equation.) b. there is no oblique asymptote. what is the equation of the horizontal asymptote of r(x)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the horizontal asymptote is. (type an equation.) b. there is no horizontal asymptote.

list all the asymptotes of the following function, then graph the function. r(x)=7/(x^2 - 36) what is/are the equation(s) of the vertical asymptote(s) of r(x)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the vertical asymptote(s) is/are x = - 6,x = 6. (use a comma to separate answers as needed. type an equation(s).) b. there is no vertical asymptote. what is the equation of the oblique asymptote of r(x)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the oblique asymptote is. (type an equation.) b. there is no oblique asymptote. what is the equation of the horizontal asymptote of r(x)? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the horizontal asymptote is. (type an equation.) b. there is no horizontal asymptote.

Answer

Explanation:

Step1: Find vertical asymptotes

Set denominator equal to 0. Given $R(x)=\frac{7}{x^{2}-36}=\frac{7}{(x + 6)(x - 6)}$. Solving $(x + 6)(x - 6)=0$ gives $x=-6$ and $x = 6$.

Step2: Determine oblique asymptote

Degree of numerator (0) is less than degree of denominator (2). So, no oblique asymptote.

Step3: Find horizontal asymptote

Since degree of numerator is less than degree of denominator, as $x\to\pm\infty$, $y = 0$.

Answer:

A. The vertical asymptote(s) is/are $x=-6,x = 6$. B. There is no oblique asymptote. A. The horizontal asymptote is $y = 0$.