Restate question: What is an example of a non-function?
The equation of a circle is x2 + y2 = r2. Since a function can only be intersected once by a vertical line, the circle is not a function (almost any vertical line through the circle will cut it twice).
If you solve the equation for y, you must write: y = +/- sqrt(r2-x2), so for each value of x there are TWO values of y.
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Y = X2 Is a parabolic function.
None.
y = cuberoot(x) for real x is not a rational function.
No. A simple example of this is y = x2; the inverse is x = y2, which is not a function.