Is a continuous function in

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f

is a continuous function in

[a, b]

g

is a continuous function in

[b, c]

. A function

h(x)

is defined as

$h(x)$	condition
$f(x)$	$\text{for } x \in [a, b]$
$g(x)$	$\text{for } x \in (b, c]$

f(b) = g(b)

, then (1)

h(x)

has a removable discontinuity at

x = b

(2)

h(x)

may or may not be continuous in

[a, c]

(3)

h(b^-) = g(b^+)

and

h(b^+) = f(b^-)

(4)

h(b^+) = g(b^-)

and

h(b^-) = f(b^+)