Q. 1 TB - Calculus

Question

What is a polynomial? What is 

the domain of every polynomial function?

Step-by-Step Solution

Answer

The domain of every polynomial function is all real numbers: (-$\infty$,$\infty$). The range of that domain depends on the type of polynomial function.

Step 1. Definition of a polynomial

A function that only uses non-negative integer powers or only positive integer exponents of a variable is referred to as a polynomial function. For example, $$3x +6$$ is a polynomial function that has an exponent equal to positive integer 1.

The general form of the polynomial:

\(f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0\)

where, \(n\epsilon \mathbb{N}\)

Step 2. The domain of a polynomial function

The collection of all possible values for a function is its domain. The domain of all the polynomial functions consists of all real numbers ranging from (-$\infty$, $\infty$).