SOLUTION: x^2+(y-1)^2=64 findin domain and range

Algebra ->  Coordinate-system -> SOLUTION: x^2+(y-1)^2=64 findin domain and range       Log On


   

Question 758079: x^2+(y-1)^2=64 findin domain and range
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Try solving for y.

(y-1)^2=64-x^2
Two separate functions together: y=1%2Bsqrt%2864-x%5E2%29 and y=1-sqrt%2864-x%5E2%29
and you can consider where y is bounded and what is x allowed to be... fine..
but you could also use graphical knowledge about this circle.

Using graphical knowledge, the center is at (0,1) and the radius is 8 units.

The circle has a range set of 1-8 to 1+8, or y is -7%3C=y%3C=9.

The domain is for the upper semicircle and for the lower semicircle, actually for TWO functions, those listed above when solved for y. The domain is the set of points -8%3C=x%3C=8