I understand everything else but I'm struggling to understand how the ranges are determined for the various regions of the circle ( upper half, lower half, left half and right half)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 43E
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I understand everything else but I'm struggling to understand how the ranges are determined for the various regions of the circle ( upper half, lower half, left half and right half) 

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