Dear student,
In an abstract Mathematical sense, a function is a mapping of some  domain onto some range.  For each item in the domain, there is a  corresponding item in the range of the function.  Thus the domain is all  of the possible inputs to the function and the range is all of the  possible outputs.  Each item in the domain corresponds to a specific  item in the range.  However, an item in the range may correspond to  multiple items in the domain.
For example, let's describe a function for album titles.  Our  function will take as its domain, album titles. Our function, let's call  it FL(album_title) will output the first letter of the first word in  the title of the album.  Thus the range of our function will be all of  the letters in the alphabet. (I'm pretty sure that you can find an album  for each letter of the alphabet, right?)  Here are some examples of our  function at work.    







Album Title
FL(Album Title)


What's The Story, Morning Glory?
W


Achtung Baby
A


The Piano Rollls3
T


Piano Man
P


August and Everything After
A


Collective Soul
C


1812 Overture
???



 
For each album title (left) there is a corresponding FL(our album  title) from the range of FL(album_title). As you can see, the function  can get the same value in the range for two different inputs.  But what  about the good old 1812 Overture?  Because the first word - "1812" -  does not start with a letter, our function cannot handle it.  Thus it is  out of the domain of our function.  Hence, the domain of FL(album  title) is all album titles that begin with a letter.