Here are the essential concepts you must grasp in order to answer the question correctly.
Equation of a Circle
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In the given equation, x² + (y - 1)² = 1, we can identify the center as (0, 1) and the radius as 1, since it matches the standard form with h = 0, k = 1, and r² = 1.
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Graphing Circles
To graph a circle, plot the center point (h, k) on the coordinate plane and then use the radius to mark points that are r units away in all directions. This creates a circular shape. For the equation provided, the circle will be centered at (0, 1) with a radius of 1, resulting in a circle that touches the points (0, 2), (0, 0), (1, 1), and (-1, 1).
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Domain and Range of a Circle
The domain and range of a circle can be determined from its center and radius. The domain is the set of x-values that the circle covers, while the range is the set of y-values. For the circle described by the equation, the domain is [-1, 1] and the range is [0, 2], reflecting the horizontal and vertical extents of the circle on the graph.
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