17. Which of the following most closely resembles the graph of y = x2/(x-1)?

A

B

C

D

E

 

 

Solution: The answer is D

 

Since y is undefined at x = 1, the graph must have a vertical asymptote at x = 1. Furthermore, since the numerator has degree exactly one more than the degree of the denominator, the graph of y has a slant asymptote at y = x + 1. Hence Since the only graph that has both a vertical and a slant asymptote is that of D, then D most closely resembles the graph of y = x2/(x-1).