The function is defined by g(x)= cases 1 x^ 2 -2x , & x<1

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The function

g

is defined by

g(x)=\begin{cases} \dfrac{1}{x^{2}-2x}, & x<1,\\ \sqrt{x+2}, & x\ge 1. \end{cases}

Which of the following statements about vertical asymptotes of

g

is correct? (a)

g

has vertical asymptotes at

x=0

and

x=2

. (b)

g

has a vertical asymptote only at

x=-2

. (c)

g

has a vertical asymptote only at

x=0

. (d)

g

has a vertical asymptote only at

x=1