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 - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 208: 22

Answer

The degree $\dfrac{1}{2}$ is not an integer. Therefore, the given function is not a polynomial.

Work Step by Step

A polynomial function is a function that has the form: $f(x)=a_n x^n +a_{n-1} x^{n-1}++a_1 x+ a_0$ Where the coefficients $(a_n, a_{n-1}..)$ are real numbers and $n$ represents a non-negative integer. We can see from the given function that the term $\sqrt x$ or, $x^{1/2}$ has a non-integer power $\dfrac{1}{2}$ . Since the degree $\dfrac{1}{2}$ is not a integer, the given function is not a polynomial.
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