The graph of a continuous function is described as follows

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The graph of a continuous function

r

is described as follows. • For

x<2

, the graph approaches a vertical asymptote at

x=2

by decreasing without bound. • For

x>2

, the graph approaches the same vertical asymptote at

x=2

by increasing without bound. • For

x\le 0

, the graph coincides with the line

y=-x+1

. • For

0<x<2

, the graph is a smooth curve connecting

(0,1)

to the asymptote such that

r(1)=3

. • For

x>2

, the graph is a smooth curve that passes through

(3,5)

and approaches the horizontal line

y=4

x\to\infty

. Answer the questions below about

r

. (a) Determine

\displaystyle \lim_{x\to 2^-} r(x)

. State your answer using appropriate limit notation. (b) Determine

\displaystyle \lim_{x\to 2^+} r(x)

. State your answer using appropriate limit notation. (c) Does

\displaystyle \lim_{x\to 2} r(x)

exist? Justify your conclusion by referring to the behavior described.