No, x²+y²= 9 does not represent y as a function of x.
For x= 0,
y²= 9
=>y= ±3,
i.e y has two values +3 and -3
Since single value of x , there are two values of y
For an equation or relation to be function every element in domain( every value of x) there should one distinct value or image in co-domain (one value of y)