A function is continuous everywhere except that is undefined and

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A function

f

is continuous everywhere except that

f(3)

is undefined and

\displaystyle \lim_{x\to 3}f(x)=2

. Define

g(x)=|f(x)|

for all

x

where

f(x)

is defined. Determine whether

g

is continuous at

x=3

and state the type of any discontinuity there.