Question

Find an expression for the function whose graph is the given curve.

The top half of the circle x^2 + (y-2)^2 = 4

Please Help. I don't even know where to start.

Answer 1

Hints:
1. Solve for y in terms of x.

2. You will have an expression involving a square-root of an expression.

3. You will need to restrict the expression under the radical to be non-negative, or else you will end up with a complex quantity.

4. For the top half of the curve (circle), restrict the value of the square-root to be non-negative, i.e. take the positive value of the square-root only.

Answer 2

So what do you mean by y in terms of x? I solved x^2 + (y-2)^2 = 4 and I got y^2 - 4y + 8 = x^2 ?

Answer 3

I would isolate y on the left like:
(y-2)²=4-x²
and take square-root on both sides.
transpose the -2 to the right and you'll get your f(x)=y=....