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 + y² = 16, it can be rewritten as (x - 0)² + (y - 0)² = 4², indicating that the center is at (0, 0) and the radius is 4.
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Graphing Circles
To graph a circle, plot the center point and use the radius to mark points in all directions (up, down, left, right) from the center. The resulting shape is a round figure where all points are equidistant from the center, allowing for a visual representation of the circle's equation.
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Domain and Range
The domain of a function refers to all possible x-values, while the range refers to all possible y-values. For the circle described by x² + y² = 16, the domain is [-4, 4] and the range is also [-4, 4], as the circle is centered at the origin and extends 4 units in all directions.
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Domain & Range of Transformed Functions