12 Piecewise Functions Example 12.1. Show solution Graph of the piecewise function equal to x cubed for x < 1 and 3x - 2 for x >= 1, through (-1,-1), (0,0), (1,1) and (3,7); a dotted line at x = 1 marks where the rule changes. The dotted line at is not a vertical asymptote; it marks where the rule switches from to . Example 12.2. Show solution Graph of the piecewise function equal to x squared for x < 0, 2 at x = 0 and 2x + 1 for x > 0: open circles at (0,0) and (0,1), a closed point at (0,2), and the points (-2,4) and (2,5). Example 12.3. Show solution