When x = 0, y=f(x) is not connected because of a simple hole that could be plugged by adding or moving one point.
When x = 1, y=f(x) is connected and smooth.
When x = 2, y=f(x) is connected and with a corner.
When x = 3, y=f(x) is not connected because of a simple hole that could be plugged by adding or moving one point.
When x = 4, y=f(x) is not connected because of a vertical jump that could not be plugged by moving one point.
When x = 5, y=f(x) is connected and smooth.
When x = 6, y=f(x) is not connected because of a simple hole that could be plugged by adding or moving one point.