goo.gl/photos/e6Ks3v4Qqj177Nun6

Question

The graph below is made from two semicircles. The domain of the function in the graph is [−8,8]
[-8,8]
. Find a piecewise formula for the function f(x)
f(x).

Help please, I already on my last attempt and any help is greatly appreciated!

Answer 1

a circle with center at (4,0) and radius 4 is

(x-4)^2 + y^2 = 16
or,
y = √(16-(x-4)^2)

The left semicircle has center at (-4,0) and radius 4, but lies below the x-axis, so

So, f(x) =
-√(16-(x+4)^2) for -4 <= x <= 0
√(16-(x-4)^2) for 0 <= x <= 4

Answer 2

Thanks Steve!