For $x > 0$, $|x| = x$, so $f(x) = -1$. For $x < 0$, $|x| = -x$, so $f(x) = -\frac{-x}{x} = 1$. The graph is therefore the line $y = 1$ for negative $x$ and the line $y = -1$ for positive $x$, which is plot A.
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