2.7.56 Function properties

Condition: Examine the function \( f(x) \) for continuity and construct its graph. \[ f(x)=\left\{\begin{array}{cc} 1, & x \leq-1 \\ |x-1|, & |x|<1 \\ x^{2}+1, & x \geq 1 \end{array}\right. \]