A circle itself is not a standard function y equals f of x because it fails the vertical line test. For most x values, a circle has two y values: one above and one below the center.
The standard equation of a circle is x minus h squared plus y minus k squared equals r squared, where h and k represent the center coordinates and r is the radius.
However, we can split a circle into two separate functions. The upper semi-circle is y equals k plus the square root of r squared minus x minus h squared. The lower semi-circle is y equals k minus the square root of r squared minus x minus h squared.
In a broader sense, circle functions refer to trigonometric functions like sine and cosine. These functions describe the coordinates of points on the unit circle as the angle theta changes.
To summarize: A complete circle is not a function because it fails the vertical line test. However, semi-circles can be expressed as functions. The upper semi-circle uses a positive square root, while the lower uses a negative square root. Additionally, trigonometric functions like sine and cosine are sometimes called circle functions because they describe coordinates on the unit circle.