Determine whether the equation defines \( y \) as a function of \( x \). \( x^{2}+(y-1)^{2}=16 \) a. no b. yes

This equation describes a circle with a center at \( (0, 1) \) and a radius of 4. Therefore, for each \( x \) value within the range of the circle (from -4 to 4), there are generally two corresponding \( y \) values (one above and one below the center). Hence, \( y \) is not uniquely determined by \( x \) for all values, making the answer: a. no. In the case of circles, a single \( x \) can lead to two \( y \) values, confirming it's not a function. Functions must pass the vertical line test, which a circle does not!