TITLE: What does it mean to extend a function?
QUESTION [23 upvotes]: What does it mean to extend a function? Can someone please give an example?
Thanks in advance!

REPLY [23 votes]: A good example might be $\sqrt{x}$.  We cannot put a negative $x$ in a square root if we only care about real numbers.  But, we can define a function $\sqrt{|x|}$.  If $x\geq 0$ this is the same function as before since, in this case, $|x|=x$.  But, the function can now take in negative numbers.