The simplest way to find the range is to graph the relation/function.

a)

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 .

a)

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 .

b)

This is a circle of radius 8, with center (2, -1). You do this one.

c)

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

-Dan