Mathematics

Problem

The graph of

y=f(x)

has an open circle at

(2,3)

and a filled dot at

(2,5)

. On both sides of

x=2

, the curve approaches the open circle smoothly. Which statement best describes

f

x=2

? a)

f

is continuous at

x=2

because

\displaystyle\lim_{x\to2}f(x)

exists b)

f

is not continuous at

x=2

because

f(2)

does not exist c)

f

is not continuous at

x=2

because

f(2)\neq\displaystyle\lim_{x\to2}f(x)

f

is continuous at

x=2

because

\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2^+}f(x)