determine the continuity of the function at

they mean the greatest integer funciton. whatever x is then you round up to the nearest whole number. so if x = 3.9 x = 4. if x = 2.000001 x = 3.

this would give a graph of a step function since it rounds up. The graph is discontinuous. I know what you mean about textbooks, thats why a teacher comes packaged with them =P

I’m pretty sure it’s the ceiling or floor function (especially the latter).

http://en.wikipedia.org/wiki/Floor_function

The floor function is the function that returns the greatest integer less than or equal to the input (i.e. it rounds down to the nearest integer). The ceiling function rounds up.