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Chapter 8: Q. 1 TB (page 679)

What is a polynomial? What is

the domain of every polynomial function?

Short Answer

Expert verified

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

Step by step solution

01

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

02

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 (-鈭�,鈭�).

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Most popular questions from this chapter

Find the interval of convergence for power series:鈭�k=0鈭�-1k2k!x2k.

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Find the interval of convergence for power series:鈭�k=0鈭�1k!xk

Show that the power series 鈭�k=1鈭�鈥�(鈭�1)kk2xkconverges absolutely when x=1and when x=-1. What does this behavior tell you about the interval of convergence for the series?
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