Since you're in the UK, I'll spare you the details.
As for the algebra, plug in a number for "x," then solve for the "y" coordinate. The results will look like the graphs mimed by the stick guy. The last one originally says "crap."
Example:
Sqrt(4) is not a surd, because it's simplified into 2. [Sqrt(4) = 2]
Sqrt(2) is a surd, because it cannot be simplified further into a whole number. [Sqrt(2) =~ 1.414213]