College Algebra (10th Edition)

Published by Pearson

Chapter 5 - Review Exercises: 3

Answer

The given function is neither a polynomial nor a rational function because it has an exponent that is not an integer.

Work Step by Step

RECALL: (1) A function $f(x)$ is a polynomial function if $f(x) = a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0$, where $a_n\ne0$ and $n$ is an integer.. (2) A function $f(x)$ is a rational function if $f(x) = \dfrac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are polynomial functions and $q(x) \ne 0$. Note that the given function is different in form than the one in (2) above. Thus, the given function is not a rational function. Although the function seems to be similar in form to the one in (1) above, it has an exponent that is not an integer, Thus, it is not a polynomial function. Therefore, the given function is neither a polynomial nor a rational function.

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