A function is represented graphically near

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

Problem

A function

f

is represented graphically near

x=2

. The graph is described as follows: • For

x<2

, the curve is a straight line segment that approaches the point

(2,3)

from below and appears to be tangent to the

x

–axis at

x=1.5

. • For

x>2

, the curve is part of a different straight line that approaches the point

(2,5)

from above and passes through

(3,8)

. • The point

(2,4)

is plotted as a solid dot on the graph. Answer the following questions about the behavior of

f

x=2

. (a) Estimate

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

using the description of the graph. (b) Estimate

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

using the description of the graph. (c) Determine whether

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

exists. Justify your conclusion in terms of the one-sided limits found in parts (a) and (b).