Polynomial and rational function modeling

In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.
Polynomial function models
A polynomial function is one that has the form
where n is a non-negative integer that defines the degree of the polynomial. A polynomial with a degree of 0 is simply a constant function; with a degree of 1 is a line; with a degree of 2 is a quadratic; with a degree of 3 is a cubic, and so on.
Historically, polynomial models are among the most frequently used empirical models for curve fitting.
Advantages
These models are popular for the following reasons.

Polynomial models have a simple form.
Polynomial models have well known and understood properties.
Polynomial models have moderate flexibility of shapes.
Polynomial models are a closed family. Changes of location and scale in the
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