Mathematics

Problem

The graph of a function

g

satisfies the following: •

\displaystyle\lim_{x\to 2^-}g(x)=-\infty

•

\displaystyle\lim_{x\to 2^+}g(x)=\infty

Which statement is most consistent with these observations? a)

g

has a horizontal asymptote at

y=2

because the value of

g

approaches 2 near

x=2

. b)

g

has a vertical asymptote at

x=2

because the one-sided limits are unbounded in opposite directions. c)

g

does not have an asymptote at

x=2

because the one-sided limits are not equal. d)

g

is continuous at

x=2

because both one-sided limits exist.