I think you are a little confused. Before you enter it in 
your calculator you must solve the equation for y:




=±

This means the equation consists of two function graphs,

One function graph is the graph of this function, using
the positive square root:

=



The other function graph is the graph of this function,
using the negative square root:





But the original equation



consiste of BOTH of these at the same time on the
same set of axes, like this:



and this is not a function because it does not
pass the vertical line test.  It is a parabola
that opens to the right.

Since the x-values of the graph start where x=1,
including that point, and the graph goes to 
infinity on the right the domain is 

Since the y-values go both upward and downward
from 0 both to positive and negative infinity,
the range is   

No, it is not a function.

Edwin