Find all horizontal and vertical asymptotes of f(x). For each vertical asymptote, determine whether or on either side of the vertical asymptote.
A) horizontal asymptote at ; there are no vertical asymptotes.
B) horizontal asymptotes at ; vertical asymptote at ;
C) no horizontal asymptote; vertical asymptote at with n an integer;
D) horizontal asymptotes at ; vertical asymptote at with n an integer;

Question

Find all horizontal and vertical asymptotes of f(x).  For each vertical asymptote, determine whether  or  on either side of the vertical asymptote.
A) horizontal asymptote at ; there are no vertical asymptotes. 
B) horizontal asymptotes at ; vertical asymptote at ; 
C) no horizontal asymptote; vertical asymptote at with n an integer; 
D) horizontal asymptotes at ; vertical asymptote at with n an integer;

Quizplus · Accepted Answer

For option A, there is only one horizontal asymptote and no vertical asymptotes. 
For option B, there are two horizontal asymptotes and one vertical asymptote. The function approaches positive infinity on one side of the vertical asymptote and negative infinity on the other side. 
For option D, there are two horizontal asymptotes and one vertical asymptote. The function approaches positive infinity on one side of the vertical asymptote and negative infinity on the other side. 
For option C, there is no horizontal asymptote and one vertical asymptote at integer values of x. The function approaches positive infinity on one side of the vertical asymptote and negative infinity on the other side. This is the best choice as it satisfies all the given conditions.

Find All Horizontal and Vertical Asymptotes of F(x)