A function has a vertical asymptote at

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

Problem

A function

f

has a vertical asymptote at

x=5

. As

x\to5^{+}

f(x)

increases without bound; as

x\to5^{-}

f(x)

decreases without bound. Which of the following statements is most strongly supported by this information? (a)

\displaystyle \lim_{x\to5} f(x)=-\infty

(b)

\displaystyle \lim_{x\to5^{-}} f(x)=\infty

(c)

\displaystyle \lim_{x\to5^{+}} f(x)=\infty

(d)

\displaystyle \lim_{x\to5} f(x)=0