(Solved): The circle in the Cartesian plane, center the origin and radius 5 units is given (by Pythagoras' Th ...

The circle in the Cartesian plane, center the origin and radius 5 units is given (by Pythagoras' Theorem) by the equation: $$x^2+y^2=25.$$ Sketch this circle. Explain with proof why this is not the graph of a function. Give three different subsets of the circle which are functions, each with domain $$[?5,5]$$ and for each describe its range, give a formula for the function and plot its graph.