Continuity · Exercise 36

Determine whether or not the given function $f$ is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.

Determine the values of $b$ and $c$ such that the following function is continuous on the entire real number line.

$$f\left(x\right)=\{\begin{array}{cc}x+1,& 1<x<3\\ x^2+bx+c,& \left|x-2\right|\ge 1\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Precalculus 2e · §12.3 Continuity · Exercise 36