A function is defined by f(x)= cases 2x+1, & x4

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

Problem

A function

f

is defined by

f(x)=\begin{cases} 2x+1, & x<4,\\ 5, & x=4,\\ 3x-7, & x>4. \end{cases}

Which statement best describes the behavior of

f

x=4

? (a)

f

is continuous at

x=4

because the left‐ and right‐hand limits are both

5

, which equals

f(4)

. (b)

f

has a jump discontinuity at

x=4

because the one‐sided limits exist but are not equal. (c)

f

has a removable discontinuity at

x=4

because the limit from both sides is

9

but

f(4)=5

. (d)

f

has an infinite discontinuity at

x=4

because the limit does not exist.