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Will any 4 points on a graph produce a Cubic equation?
Any 4 points in the Cartesian plane determine a unique equation that is of degree at most three (i.e., a "cubic" equation). It is, of course, possible that the 4 points actually lie on a degree two ("quadratic"), a degree one ("linear"), or a degree zero ("constant") equation. However, if the 4 points do not lie on a constant, linear, or quadratic curve, then they will like on a unique cubic curve. In general, N points will determine a unique curve of degree at most (N-1).
What is the unique possible lowest number?
1/0
What is unique about the linear function?
Each variable has an exponent equal to one.
A relation in which every x-value has a unique y-value?
A Function
How do you tell if an equation is a function?
Let's assume (for simplicity) that "y" is a function of "x". That means that for every value of "x", there is a unique value of "y". In this case, if the equation can be solved for "y", it is a function. Some equations are difficult or impossible to solve explicitly for "y"; in this case, "y" may still be a function of "x", if for every value of "x" only a single value of "y" is possible for the equation. However, if this is the case, it may be difficult to verify.
