\textbf{117.} Suppose $f(x) = \begin{cases} (x-1)|x| & ; \ |x-1| < 1 \\ x^2 + ax + b & ; \ |x-1| \geq 1 \end{cases}$ is always a continuous function. What is the value of $a$?
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(1) $\dfrac{3}{2}$ \hfill (2) $-1$ \hfill (3) $1$ \hfill (4) $\dfrac{5}{2}$
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