The function is defined by f(x)= cases x+2, & x1

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

Problem

The function

f

is defined by

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

Which of the following correctly describes the behavior of

f

x=1

? (a)

\displaystyle \lim_{x\to 1} f(x)=4

because

f(1)=4

. (b)

\displaystyle \lim_{x\to 1} f(x)

does not exist because

f

is undefined at

x=1

. (c)

\displaystyle \lim_{x\to 1^{-}} f(x)=3\text{ and }\lim_{x\to 1^{+}} f(x)=4

. (d)

\displaystyle \lim_{x\to 1^{-}} f(x)=4\text{ and }\lim_{x\to 1^{+}} f(x)=3