PrecalculusChallengeFunctions and Their Graphs

Functions and Their Graphs · Challenge problem

Find the constants $a$ and $b$ that make $f$ continuous for all real $x$ :

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