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What is the difference between a power functions and a polynomial functions?
A power function is of the form xa where a is a real number. A polynomial function is of the form anxn + an-1xn-1 + ... + a1x + a0 for some positive integer n, and all the ai are real constants.
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
What are the properties of rational functions?
Such functions are defined as one polynomial divided by another polynomial. Their properties include that they are defined at all points, except when the denominator is zero. Also, such functions are continuous at all points where they are defined; and all their derivatives exist at any point where they are defined.For more details, I suggest you read the Wikipedia article - or some other source - on "Rational function".
How does polynomial function exist in real life?
As with most advanced math, if your "real life" involves engineering work, you will use such math; otherwise, you will hardly have anything to do, in this case, with polynomial functions.
What are the conditions that an algebraic expression is not a polynomial?
Basically, an expression is not a polynomial when anything is done that is not allowed in a polynomial - for example, use any variable in the denominator of a monomial, use non-integral powers or radicals (which is basically the same as a non-integral power), use functions, etc.
