1. The problem is to find the range of the function defined by the equation of a circle: $$(x-1)^2 + (y-3)^2 = 16$$. 2. This is the equation of a circle with center at $(1,3)$ and radius $4$ because $16 = 4^2$. 3. The range of $y$ values on this circle is the set of all $y$ such that the point $(x,y)$ lies on the circle. 4. Since the circle is centered at $y=3$ and has radius $4$, the lowest $y$ value is $3 - 4 = -1$ and the highest $y$ value is $3 + 4 = 7$. 5. Therefore, the range of $y$ is $$[-1, 7]$$. 6. In plain language, the circle extends 4 units above and below its center along the $y$-axis, so the $y$ values go from $-1$ up to $7$.