The graph of a function satisfies the following: • • Which statement is most…

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

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.