Since $|-x| = |x|$, the equation can be rewritten as $y = 3|x| + \frac{1}{2}$.
This is an absolute value function of the form $y = a|x - h| + k$, where $a = 3$, $h = 0$, and $k = \frac{1}{2}$.
The vertex of the graph is $(h, k) = (0, \frac{1}{2})$.
The graph opens
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