Question

What is the relationship between power functions and polynomial functions

Answer 1

Answer:

• A power function is basically a variable base raised to a number power. For example, a power function is basically a function where $y\:=\:x\:^n$ where n is any real constant number.

• Polynomial functions are basically a sum of power functions - nothing more than that.
• Polynomials have certain properties which are really power-like.
• When a variety of different power functions get added together, polynomials tend to take on certain unique behaviors.
• A polynomial may comprise of a large number of power functions, but on of them will dominates all others eventually.

In a nutshell, the end behavior of both power function represented by the leading term - the term containing the highest power of the variable is called the leading term of the function - is very much is the same as the end behavior of a polynomial function.

Keywords: power function, polynomial

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