is a function, 

because no matter what value you substitute for x, there
will be just one value for y.  The graph looks like this



It passes the vertical line test. That is,

when you pass vertical lines (the green one below):





none of those vertical intersects the graph more than once.


but  is not... can you say why?

Let's solve it for y:





The  tells us that when we substitute a
value for x there will be two values for x, one with
a + sign and one with a - sign.  For example when the
single value 2 is substituted for x we get:



The graph looks like this



It does not pass the vertical line test, because

when you pass vertical lines (the green one below)

through the graph:



many of those vertical intersect the graph more than once.

Edwin