The function is defined by r(x)= cases ax+1,& x<1

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

Problem

The function

r

is defined by

r(x)=\begin{cases} ax+1,& x<1,\\ b,& 1\le x<3,\\ 5-x,& x\ge 3. \end{cases}

Determine the constants

a

and

b

so that

r

is continuous at both

x=1

and

x=3