\textbf{112.} The graph shown is the graph of $y = 1 + a\sin bx \cos bx$. What is $a + b$?
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\textit{[Figure: Graph of $y = 1 + a\sin bx\cos bx$ showing a sinusoidal curve with amplitude markings at $\frac{3}{2}$ and $1$, and $x$-axis markings at $-\dfrac{\pi}{4}$ and $\dfrac{3\pi}{4}$]}
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(1) $1$ \qquad
(2) $\dfrac{3}{2}$ \qquad
(3) $2$ \qquad
(4) $3$
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