Answer
The equation DOES NOT define $y$ as a function of $x$.
Work Step by Step
Solve for $y$ in terms of $x$ to have:
$(y-1)^2=-x^2+4
\\y-1=\pm \sqrt{-x^2+4}
\\y= 1 \pm \sqrt{-x^2+4}$
The last equation is a rule that gives two values of $y$ for some values of $x$ (e.g., x=1, x=0).
Thus, it does not define $y$ as a function of $x$
