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: 17


It is a polynomial $f(x) =\dfrac{-x^2}{2}+\dfrac{1}{2}$ of degree: $2$ Leading term: $\dfrac{-1}{2}x^2$ Constant: $\dfrac{1}{2}$

Work Step by Step

We re-arrange the given function as follows: $g(x)=\dfrac{-x^2}{2}+\dfrac{1}{2}$ A polynomial can be defined as a function containing only terms where $x$ is raised to a positive, integer power or constant. We can see from the given function that it is a polynomial. The degree is equal to the power of the term with the highest power, so the degree is $2$. Also, the constant value is $0$. The term with the highest degree is always known as the leading term; that is, $4x^4$. So, it is a polynomial $f(x) =\dfrac{-x^2}{2}+\dfrac{1}{2}$ of degree: $2$ Leading term: $\dfrac{-1}{2}x^2$ Constant: $\dfrac{1}{2}$
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