Consider the function Which one of the following conditions on and is necessary and…

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

Problem

Consider the function

f(x)=\begin{cases}px+1, & x<3,\\4x+q, & x\geq3.\end{cases}

Which one of the following conditions on

p

and

q

is necessary and sufficient for

f

to be continuous at

x=3

? (a)

p+1=12+q

(b)

3p=12+q

(c)

3p+1=12+q

(d)

3p+1=4p+q