\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For each of the following functions on \([0, 2]\), state whether it is (a) a step function, (b) piecewise continuous, (c) neither:
  1. \(f(x) = \lfloor 2 x \rfloor\);
  2. \(g(x) = \sin(\pi x)\);
  3. \(h(x) = 1/(x - 1)\) for \(x \ne 1\), \(h(1) = 0\).

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