CalculusSuperchallengeLimits and Continuity

Limits and Continuity · Superchallenge problem

Find constants $a$ and $b$ so that $f$ is continuous for all real $x$ :

f(x)=\begin{cases} x+1, & x<1,\\[2pt] ax+b, & 1\le x<2,\\[2pt] 3x-2, & x\ge 2.\end{cases}