Find all vertical asymptotes and create a rough sketch of th

Find all vertical asymptotes and create a rough sketch of the graph near each asymptote. f(x)=x + 2/x^2 -4 There is a vertical asymptote at x = (Type an integer or a simplified fraction. Use a comma to separate answers.) Which graph best represents the behavior of f(x) near the vertical asymptote(s)? Choose the correct graph below.

Solution

f(x) = (x+2)/(x^2 -4)

Vertical asymtote : plug denominator =0

x^2 - 4=0

x = -2 ; x=2

So, Graph does not cross or pass x= -2 , x=2

Graph Option A is correct