I probably don't understand intervals well enough yet, but if

x = new interval[-2,2]
[-2,2]

and

x^2
[0, 4]

then why doesn't abs[x] yield [0,2]?

Further, why doesn't abs[x+2] => [0, 4]?

I would have thought that applying "abs" to all values in the interval would
have yielded the subrange of [0,2].

Instead, it appears that abs[] is applying the operation to only the end points,
and not the entire interval. Then, because the absolute value of the end points
are the same value, the range collapses to the single value.

However, this is apparently not the case for:

abs[x + 2]

which I would have thought as: [0, 4], but it's not: it's 4.

And, if one uses intervals with mean values:

y = new interval[-2, 0, 2]
[-2, 0, 2]
abs[y]
2
abs[y+2]
4

what happened to the abs[] on the lower bound of the interva?