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

The top half of the circle x^2 + (y - 3) ^2 = 4

We can accomplish this by:

(y-3) ^2=4-x^2

Now, lets take the square root of both sides:

y-3=±sqrt (4-x^2) y=±sqrt (4-x^2) + 3

Now, we only need the top half or the positive half so this means that our answer is simply:

y=sqrt (4-x^2) + 3