Why are all polynomials in one variable functions?

Question

This is an explanation question needed to be answered. Please include the meanings of polynomial and function in one variable. Thank you!

Answer 1

A polynomial in one variable is an expression that is the sum of some number of terms, where each term is the product of some constant times the variable raised to some non-negative power.

 

A function of one variable is a relation in which any possible value of the variable is related to no more than one other value.

 

So a function is like a machine.  You put something in (a value for the "independent variable", for example), and you get something out.  Sometimes you don't get anything out, such as if the value you put in is not in the domain of the function.  But you can never get more than one thing out for each thing you put in.

 

So when you put a value in for the variable in a polynomial, each term can only take on one specific value, and when you add all the terms together, they still can only add up to one value.