Polynomials and non polynomials how different?

Answer 1

Well, "non-polynomial" can be just about anything; presumably you mean a non-polynomial FUNCTION, but there are lots of different types of functions. Polynomials, among other things, have the following properties - assuming you have an expression of the type y = P(x):* The polynomial is defined for any value of "x".

* The polynomial makes is continuous; i.e., it doesn't make sudden "jumps".

* Similarly, the first derivative, the second derivative, etc., are continuous.

A non-polynomial function may not have all of these properties; for example:

* A rational function is not defined at any point where the denominator is zero.

* The square root function is not defined for negative values.

* The first derivative (i.e., the slope) of the absolute value function makes a sudden jump at x = 0.

* The function that takes the integer part of any real number makes sudden jumps at all integers.