I believe what this question is saying (albeit poorly) is that you have 4 possible ways to encode what happens on a given interval between critical points, and not that the sequence you would submit as an answer consists of 4 digits.
For a basic example, let's consider

. We have

so that

is the only critical point, and

so that

is the only inflection point.

for all

, while

for

, and vice versa.
We have two intervals to work with,

and

. So in this case, the answer would be 2 over

and 1 over

.
That's a guess at any rate. Also, I don't know how helpful this is 4 days after the fact...