Math (Semicircle)(Pre-calc)

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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!

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  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

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  2. Thanks Steve!

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