y = |x|

Yes it's a function because for any value you substitute for x
there is JUST ONE value for y, never two or three or more than one.
That's because there in JUST ONE absolute value of any number.

When you graph it you get this nice V-shaped graph:



It PASSES the vertical line test.  Look at all these
green vertical lines below.  Not a one of them crosses the graph 
more than JUST ONE TIME!:



That's how you can tell that it is a function.

Now take a look at a graph which is NOT a function,

say the graph of this parabola:
      ___
y = ±Öx-5



As you can see there are two values for y for many of
the values of x.  The green vertical lines, if they cross
cross it at all, they cross the graph twice, except for
the one at -5, which only crosses it once.  But if any vertical
line crosses a graph more than once, then the graph cannot
represent a function.  This one FLUNKS the vertical line 
test, as you can see below:  



This one is not a function, but indeed y = |x| IS a function.

Edwin