A function is represented graphically as follows

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A function

f

is represented graphically as follows. • For

x<2

, the graph is the line segment joining the points

(0,0)

and

(2,3)

. • For

x>2

, the graph is the curve

y=3-(x-2)^2

drawn for

2<x<4

. • At

x=2

the point

(2,3)

is shown as an open circle, while the point

(2,1)

is shown as a solid dot. Answer the following questions about

f

. (a) Determine

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

and explain your reasoning based on the given graph. (b) State the value of

f(2)

. (c) Compare your answers to parts (a) and (b). Explain why they are different and discuss the implications for the continuity of

f

x=2