- #1
shintashi
- 117
- 1
So if i take the rules that a straight vertical line drawn through the function with more than one intersection implies it is not a function, to mean that the quadratic equation for a circle is not a function.
Furthermore, it also implies a cubic equation, such as x^3 can be a function, because the solutions will not have both a positive and negative. And if I am to generalize, it can be said that all even powers, quartic functions, etc., i.e., if the power is such that the equation has x^2, x^4, x^6, x^8, etc., then it is NOT a function,
but lacking any of those if an equation has odd powers, X^1, X^3, X^5, X^7, etc., any of these or combinations would generally be a function? So X^4+X^2 would be NOT a function, while X^7+X^3+nX^1 etc. would be, and if we mix the odd and even, the even powered variables automatically cause the whole equation to fall outside of a function, thus x^5+X^4+X^3 is canceled as a function because of the X^4.
is there anything else i should look for in identifying the differences?
Furthermore, it also implies a cubic equation, such as x^3 can be a function, because the solutions will not have both a positive and negative. And if I am to generalize, it can be said that all even powers, quartic functions, etc., i.e., if the power is such that the equation has x^2, x^4, x^6, x^8, etc., then it is NOT a function,
but lacking any of those if an equation has odd powers, X^1, X^3, X^5, X^7, etc., any of these or combinations would generally be a function? So X^4+X^2 would be NOT a function, while X^7+X^3+nX^1 etc. would be, and if we mix the odd and even, the even powered variables automatically cause the whole equation to fall outside of a function, thus x^5+X^4+X^3 is canceled as a function because of the X^4.
is there anything else i should look for in identifying the differences?