Question 642585
A relation is not a function if it assigns more than one y value to any x value in its domain.
For x=0, the equation gives us y=2 and y=-2.
That is enough to say that the equation does not represent y as a function of x.
In fact, the equation represents a circle centered at (0,0) with radius 2.
For any x such that {{{-2<x<2}}}, the equation assigns two values of y.
If you just had the graph corresponding to that equation,
{{{drawing(300,300,-3,3,-3,3,
grid(1),
blue(circle(0,0,2)),
green(line(0.5,-3,0.5,3)),
locate(0.6,1,x=0.5)
)}}}
you would know that it is not a function because there is a vertical line x=k that crosses the graph at two points.
(There is really an infinite number of such lines, but one is enough to prove it's not a function).