Give the location of the vertical asymptote(s) if they exist, and state whether function values will change sign (positive to negative or negative to positive) from one side of the asymptote to the other.
A) x = 1, no
B) x = 1, yes
C) x = -4, no; x = 1, no
D) x = -4, yes; x = 1, yes

Question

Give the location of the vertical asymptote(s) if they exist, and state whether function values will change sign (positive to negative or negative to positive) from one side of the asymptote to the other. 
A) x = 1, no 
B) x = 1, yes 
C) x = -4, no; x = 1, no 
D) x = -4, yes; x = 1, yes

Quizplus · Accepted Answer

Option D indicates that there are vertical asymptotes at x = -4 and x = 1, and the function values will change sign from one side of the asymptote to the other. This is because when x is slightly less than -4 or slightly greater than 1, the denominator of the function approaches 0 which makes the function value approach infinity. As a result, when approaching from the left or the right of the asymptotes, the function value will have different signs. Therefore, option D is the best choice.

Give the Location of the Vertical Asymptote(s) If They Exist