The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates. The second example is not a function, because it contains the ordered pairs (1,2) and (1,5). These have the same first coordinate and different second coordinates.
Q&A. Can more than one formula from a piecewise function be applied to a value in the domain? No. Each value corresponds to one equation in a piecewise formula.