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

(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 $b(x) \ne 0$. We can see that the given function has the same form as defined in the definition (b). So, the given function is a rational function. The function is not a polynomial function because it contains a variable in the denominator.