Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Chapter Review - Review Exercises - Page 267: 4

Answer

Polynomial function with degree $0$.

Work Step by Step

(a) A function $f(x)$ is said to be a polynomial function when $f(x) = a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}++a_1x+a_0$, where $a_n\ne0$. (b) A function $f(x)$ is said to be a rational function if $f(x) = \dfrac{a(x)}{b(x)}$ where $a(x)$ and $b(x)$ are known polynomial functions and $b(x) \ne 0$. The function is not a ratio of polynomials, so it is not rational. We see that the given function is a polynomial with degree $0$ because the power of $x$ is zero. That is, $3=3x^0$.
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