This is a circle of radius 7, with center (-2, 3), so the y value is between 3 - 7 = -4 and 3 + 7 = 10. Thus the range is .
This can be modified to
Thus the minimum value of the quadratic function is 4, so the minimum m value is 2. There is no upper limit on the radicand, so the upper "value" of m is . Thus the range is .
This is a circle of radius 8, with center (2, -1). You do this one.
This is a bit trickier to see what to do, so I graphed it. (See below.)
The minimum value of the range is apparently 3. The peak of the function is at x = 1/2 (we can prove this with Calculus, but you can also see it on the graph), so the maximum y value is
So the range is