We are asked to decide if the expression:
x^2 + y^2 = 1 represents a function.
We recall that in order to have a function, we need for a given value of x to have a SINGLE value of y associated with it.
So in this case, when x is 0 for example, we have the following:
0^2 + y^2 = 1
then y^2 = 1
and we realize that there are TWO values of y whose square form gives 1 (one is 1 and the other -1) Therefore, this relationship is NOT a function, since for example when x = 0 there are TWO values of y to which that x is associated (y = 1 and y = -1).
So please select that this is NOT a function for your answer.