I'm not a doctor, but I'll try.  First of all, there are other things
besides near/far-sightedness that go into acuity, and acuity is
measured at both near and far.  Having said that, ideally, the eye is
in a relaxed accomodative state when looking at distance.  To see
close, the muscles of the eye actively do things to bring things into
focus.  For a farsighted person, accomodation is required already to
see at distance (their relaxed state is looking beyond infinity).  This
limits their ability to see close (since there is a limited range of
accomodation), but if it's bad enough, it would be possible that they
couldn't even accomodate enough to see far away.

Hopefully that makes some sense.  Someone else will chime in if I said
something that isn't correct.

I know a few people who are farsighted and wear glasses full time.  I
asked one how the vision was at distance with no glasses and he said he
couldn't see.  He could be very far sighted, or maybe he has
astigmatism correction too and didn't know about it.

--

Dear Concerned Parent,

Part of this problem is the definition of the refractive STATES
of the fundamental eye.  The word "farsighted" has TWO
meanings for all practical purposes.

the refractive STATES of the natural eye are defined as follows.

The only NORMAL eye must have a refractive STATE of
EXACTLY ZERO.

A negative refractive STATE is myopia.

A positive refractive STATE is farsighedness.

This is the absolute definition of the natural eye.

Thus your children are either farsighed or myopic,
as long as you do not properly define the refractive
states of the natural eye.  This is why there
is so much confusion about the word "farsighed".

Best,

Otis

It depends on age, because focusing ability decreases with age.

Three diopters of farsightedness might go unnoticed in a 10-year-old. At age
55, the same three diopters would limit near vision dramatically, but it
would reduce _distance_ vision as well, to something like 20/100.

-MT, OD