Suppose is defined for all sufficiently large and

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

Problem

Suppose

f

is defined for all sufficiently large

x

and

\displaystyle\lim_{x\to\infty}f(x)=7

. Which of the following statements must be true? (a) The graph of

f

crosses the line

y=7

at most once. (b) For all sufficiently large

x

f(x)=7

. (c) The right end of the graph of

f

approaches the line

y=7

x\to\infty

. (d) The graph of

f

has the horizontal asymptote

y=7

x\to -\infty

and as

x\to \infty