Mathematics

Problem

Which of the following best describes what it means for the graph of a function

f

to have a vertical asymptote at

x=7

? a) Both

\displaystyle \lim_{x\to7^-}f(x)

and

\displaystyle \lim_{x\to7^+}f(x)

are infinite. b)

f(7)

is undefined while

\displaystyle \lim_{x\to7}f(x)

exists and is finite. c) At least one of

\displaystyle \lim_{x\to7^-}f(x)

\displaystyle \lim_{x\to7^+}f(x)

is infinite. d)

\displaystyle \lim_{x\to7^-}f(x)\neq\lim_{x\to7^+}f(x)

, so the two-sided limit does not exist.