The function is graphed in the -plane

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The function

g

is graphed in the

xy

-plane. At

x=3

the graph shows an open circle at

(3,5)

and a filled dot at

(3,2)

. As

x

approaches

3

from either side, the

y

-values of the graph approach

5

. Which of the following is the value of

\displaystyle\lim_{x\to3}g(x)

? (a)

2

(b) The limit does not exist because

g

is undefined at

x=3

. (c)

5

(d) The limit does not exist because the left- and right-hand limits are different.