Subject Test Question:

If f(x)=[2x]-4x with domain 0≤x≤2, then f(x) can also be written as

A) 2x
B) -x
C) -2x
D) x^2 – 4x
E) none of the above

I have to assume that [2x] means the greatest integer function (AKA the floor function)? I have not seen this on a real Subject Test, but I know it appears in at least one prep book. In short, don’t worry yourself too much about it, but it basically means that you take the greatest integer less than what’s in the bracket. So [3.4], [3], and [3.9] all equal 3.

The simple presence of that [2x] means you won’t have a continuous function, so you know right away that the answer must be none of the above. Here’s what the graph would look like, just in case you’re curious.