Question

Which statement describes the behavior of the function f(x)= 2x 3? 1- x2

Answer 1

Answer:

              2x

f(x) = -------------- or   f(x) = 2x / (1-x^2)

          1 - x^2

to eliminate any ambiguity.  The graph of this function passes thru the origin (0,0) and has vertical asymptotes at x = -1 and x = + 1.  The function is negative on (-1,0) and positive on (0,1).  

Additionally, there are two horizontal asymptotes.   As x grows large and negative, f(x) approaches zero from above.  As x grows large and positive, f(x) approaches zero from below.