In the paper we present an exhaust discussion of
the relations between Darboux-like
functions within the classes of Baire one, Baire two,
and additive functions
from **R**^{n} into **R**.
In particular we
construct an additive extendable discontinuous function
f:**R**-->**R**,
answering a question of Gibson and Natkaniec
(*Darboux like functions,*
Real Anal. Exchange **22** (1996--97), 492-533),
and show that there is no similar function
from **R**^{2} into **R**.
We also describe a Baire class two
almost continuous function f:**R**-->**R** which is not extendable.
This gives a negative answer to a problem of Brown, Humke, and Laczkovich
(*Measurable Darboux functions,*
Proc. Amer. Math. Soc. **102** (1988), 603-610).

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**Last modified April 6, 2000.**