and
can be numbers or variables, but in methods you'll most likely get one being a number and the other being a variable.
The relevance of the note is that you're really turning the modulus function into a hybrid function, by splitting the modulus up into two sections of the original function which it effects differently (due to one being below the
axis and the other being above the
axis, including zero). The modulus function will take any outputs that are negative, so below the
axis (in this case the 'inside of the modulus' is negative when
), and it will 'flip' what you have in the
axis so that you end up with the same magnitude of what you had, but with a positive sign (e.g. if you had -2, then you would get
if you have
, where you know that
is negative, then you're going to flip it across the
axis for the domain for which this is satisfied, that is for
,
). When the original function is above the
axis (or zero), that is when
is positive or zero, (i.e.
, then the modulus has no effect on the function and you get out exactly what you put in. That is for
, so
,
.
Hope that helps
EDIT: I should note here that after the flip in the
axis you need to remember to translate the graph 1 unit upwards.
EDIT2: Rephrased jibberish a bit.